Method for constructing dynamic response prediction model of bridge pier under ship impact

Abstract

This invention discloses a method for constructing a predictive model of the dynamic response of a bridge pier under ship impact. The method includes: dividing the path of the impact force from the impact location to the response location into multiple main elements, and adding boundary elements and boundary conditions; constructing a modeling path with the fewest bifurcations based on each element and boundary condition; determining the dynamic response type of each boundary element, and constructing the transfer equations of the dynamic state of each element and the dynamic equations under ship impact; sequentially concatenating the transfer equations of each element along the modeling path to obtain the overall transfer equation of the bridge pier, and solving for the augmented characteristic vectors of the bridge pier in each vibration mode; sequentially concatenating the dynamic equations of each element along the modeling path to obtain the dynamic equation of the bridge pier, calculating the generalized coordinates of the bridge pier in each mode based on this equation, and calculating the dynamic response of the bridge pier. This embodiment can clearly define the spatial action mechanism of ship-bridge collisions, thereby quickly predicting the dynamic response of bridge piers under ship impact.

Description

Technical Field

[0001] This invention relates to the field of bridge safety technology, and in particular to a method for constructing a predictive model of the dynamic response of bridge piers under ship impact. Background Technology

[0002] With the continuous advancement of large-scale cross-river and cross-sea bridge projects, the increasing size of navigable vessels, and the complex changes in the water environment around bridges, the risk of collisions between ships and bridges has significantly increased. In the event of a collision, a massive transient lateral impact force will act on the bridge structure, and the impact energy will rapidly spread along the structural transmission path, easily causing attenuation of the bridge's critical components, localized damage, or even overall fracture, potentially leading to bridge collapse. Therefore, to improve the safety and durability of bridges, the field of bridge engineering urgently needs to clarify the mechanism of ship-bridge collisions to provide effective data support for collision-resistant design and protection technologies.

[0003] Existing technologies for ship-bridge collision response primarily focus on the design of anti-collision devices, impact force calculation, and early warning system development. Most of these methods rely on numerical simulations to obtain structural response data, with very little exploration of the collision mechanism itself. However, numerical simulations are extremely time-consuming and impractical for engineering applications. Furthermore, existing theoretical calculation methods are largely limited to planar structures and cannot reflect three-dimensional spatial interactions. Therefore, clarifying the spatial mechanism of ship-bridge collisions to rapidly predict the dynamic response of bridge piers under ship impact has become a pressing issue. Summary of the Invention

[0004] This invention provides a method for constructing a predictive model of the dynamic response of a bridge pier under ship impact, in order to solve the above-mentioned problems.

[0005] In a first aspect, embodiments of the present invention provide a method for constructing a prediction model of the dynamic response of a bridge pier under ship impact, comprising:

[0006] Obtain the impact location of the ship on the bridge pier, and the location of the dynamic response to be predicted;

[0007] Along the transmission path of the impact force from the impact location to the response location, compare the cross-sections of the pier structure, draw a dividing line at the point where the cross-section changes, and divide the pier structure through which the transmission path passes into multiple main elements; according to the external connection of the main elements at both ends of the transmission path, add boundary elements and boundary conditions; based on each element and boundary condition, construct the modeling path with the fewest bifurcations.

[0008] Based on the dimensions of each main component along the modeling path, the ship's impact direction, and another direction perpendicular to the modeling path and the ship's impact direction, determine the dynamic response type of each main component; based on the position, structure, and connection of each boundary component with the boundary conditions, determine the dynamic response type of each boundary component.

[0009] Based on the dynamic response type of each component, the transfer equations of the dynamic state of each component and the dynamic equations under ship impact are constructed respectively.

[0010] The transfer equations of each component are sequentially assembled along the modeling path to obtain the overall transfer equation of the pier; based on the overall transfer equation of the pier, the characteristic vectors of each component under each vibration mode are determined; the characteristic vectors of each component are sequentially assembled along the modeling path to obtain the augmented characteristic vectors of the pier under each vibration mode.

[0011] The dynamic equations of each component are sequentially assembled along the modeling path to obtain the dynamic equation of the pier. Based on the dynamic equation of the pier, the generalized coordinates of the pier under each mode are calculated, and the dynamic response of the pier is calculated based on each augmented characteristic vector and the generalized coordinates.

[0012] In a second aspect, embodiments of the present invention provide an electronic device, the electronic device comprising:

[0013] One or more processors;

[0014] Memory, used to store one or more programs;

[0015] When the one or more programs are executed by the one or more processors, the one or more processors implement the method for constructing a prediction model of the dynamic response of a bridge pier under ship impact as described in any embodiment.

[0016] In summary, this invention provides a method for constructing a predictive model of the dynamic response of a bridge pier under ship impact. The method first discretizes the complex bridge pier system into multiple modeling elements through path analysis and dimensional analysis. Then, based on the significant differences in macroscopic scale and stiffness of bridge engineering, the dynamic response type of each modeling element is determined. Next, frequency characteristic equations are established using the state vector transfer matrix between elements and system boundary conditions to obtain the natural frequencies of the bridge pier and the characteristic vectors of each element. Based on this, the ship impact force time history is introduced as an external excitation to construct the dynamic response equations of the entire bridge pier system. Finally, the characteristic vectors of each element are extracted to construct an augmented feature space. Through coordinate transformation, the originally coupled physical space dynamic equations are transformed into independent modal equations for solution, ultimately obtaining the accurate dynamic response process of the bridge pier in the time domain. Based on the above process, the method of this embodiment can achieve the following beneficial effects:

[0017] 1. The method in this embodiment addresses the current situation where the dynamic response of ship-bridge collisions mainly relies on numerical simulation technology. Based on the dynamic state transfer equation and dynamic equation, a novel dynamic response prediction model is proposed. This model can quickly predict the dynamic response of ship-bridge collisions with a small number of equations, thus solving the shortcomings of large computational load and slow prediction speed in numerical simulation.

[0018] 2. The method in this embodiment fully considers the spatial geometric features of the structure in the modeling process, taking into account the rotation, bending and vibration of the structure in space. Compared with the simplified planar structure in traditional theory, it is more in line with the actual situation and can better describe the dynamic response characteristics of the structure under ship impact.

[0019] 3. The method in this embodiment does not require the establishment of the overall dynamic equation of the pier. The overall transfer matrix and dynamic equation of the pier can be obtained by assembling the transfer matrix and dynamic equation of the individual components. The dynamic response modeling is more flexible, and the matrix order of the chain system depends on the order of the component transfer matrix, resulting in higher solution efficiency.

[0020] 4. The method in this embodiment provides a way to divide modeling elements according to structural dimensions and determine the dynamic response type of each element. It is applicable to civil engineering structures such as bridges that have significant differences in macroscopic scale and stiffness. This method automatically determines a reasonable element division method and a reasonable dynamic response type for each element through path analysis and dimensional analysis. It does not rely on engineering experience or prior structural information, thus improving the automation of modeling and facilitating the realization of the bridge pier dynamic response prediction in this embodiment. Attached Figure Description

[0021] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 This is a flowchart of a method for constructing a prediction model of the dynamic response of a bridge pier under ship impact, provided by an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram of a bridge pier provided in an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of a modeling path for the dynamic response of a bridge pier provided in an embodiment of the present invention;

[0025] Figure 4 This is a schematic diagram of a dynamic model of a ship-bridge collision provided in an embodiment of the present invention;

[0026] Figure 5 This is a flowchart of another method for constructing a prediction model of the dynamic response of a bridge pier under ship impact, provided by an embodiment of the present invention;

[0027] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0029] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0030] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0031] Figure 1 This is a flowchart illustrating a method for constructing a predictive model of the dynamic response of a bridge pier under ship impact, provided by an embodiment of the present invention. This method is applicable to predicting the dynamic response of a single bridge pier under ship impact and is executed by electronic equipment. Figure 1 As shown, the method specifically includes:

[0032] S110. Obtain the impact location of the ship on the bridge pier, as well as the location of the dynamic response to be predicted.

[0033] In this embodiment, a pier refers to one of several identical units after dividing the entire bridge along the beam extension direction, with the pier body as the unit. Each pier, centered on the pier body, comprises multiple structures from bottom to top, including pile foundations, pile caps, the pier body itself, and the pier top beam, etc. Figure 2 As shown. In this embodiment, dynamic response refers to displacement, including translational displacement in a two-dimensional plane and rotational displacement in three-dimensional space. This embodiment will take a single bridge pier as the object and predict the dynamic response of the bridge pier under ship impact.

[0034] To clarify the mechanism of ship impact on bridge piers, this step first identifies the location of the impact and the most important response location in dynamic response prediction. Typically, the impact point is the pier cap, while the most important response location in dynamic response prediction is the top of the pier (i.e., the displacement at the pier top is of utmost concern, as this displacement directly relates to the risk of beam collapse and is a crucial parameter in bridge design). This embodiment will start from these two key locations to trace the response mechanism of the bridge pier under ship impact.

[0035] S120. Along the transmission path of the impact force from the impact position to the response position, compare the cross-sections of the pier structure, draw the dividing line at the point where the cross-section changes, and divide the pier structure through which the transmission path passes into multiple main elements; according to the external connection of the main elements at both ends of the transmission path, add boundary elements and boundary conditions; according to each element and boundary condition, construct the modeling path with the fewest bifurcations.

[0036] This embodiment calculates the pier response based on the transfer equations of dynamic state. To improve accuracy, the entire pier is first divided into components, facilitating subsequent calculations based on the dynamic response characteristics of each component. Specifically, given the significant differences in macroscopic scale and relative stiffness of bridge structures, this embodiment divides the components based on the geometric features of the structure to reflect the differences in dynamic response caused by different geometric dimensions. For example, for large-volume, heavy concrete members with similar three-dimensional dimensions, their structural stiffness is extremely high, and their internal elastic deformation under dynamic action is negligible, primarily exhibiting overall spatial translation and rotation. In contrast, slender members with a high slenderness ratio show significant elastic deformation in bending, shearing, and torsion during dynamic response, requiring consideration of the coupling effect between internal force distribution and deformation. These stiffness differences due to significant dimensional variations prompt this embodiment to divide the entire pier into multi-scale components based on structural dimensions to accurately reproduce the true structural dynamic response characteristics, thereby improving the prediction accuracy of subsequent methods.

[0037] In one specific implementation, this embodiment first determines the transmission path of the impact force from the impact location to the response location. For the structures along this path (such as pile caps and piers), their dynamic response process needs to be focused on to improve the accuracy of dynamic response prediction. For structures outside this path (such as pile foundations and beams), only the external influence of these structures on the structures along the transmission path needs to be considered, while other dynamic response characteristics (such as how these structures respond internally) can be simplified or ignored.

[0038] Optional, combined Figure 2The transmission path of the impact force from the impact location to the response location is shown by the black dashed arrow. In this embodiment, the path is traversed along the direction of the arrow, passing through cross-sections of the structure perpendicular to the path (cross-sections are shown as...). Figure 2 As shown by the green dashed lines, the figure exemplarily displays cross-sections at three locations. Whenever a significant change occurs in the cross-section, a dividing line is drawn at the point of change to indicate a clear difference in the dynamic response characteristics at either end of the dividing line. Figure 2 The red dashed line in the diagram represents a dividing line. Optionally, the cross-section at each location in the structure can be projected onto a plane perpendicular to the conduction path, using the conduction path as the axis. The intersection-to-exclusion ratio (IoU) of the projected cross-sections at two adjacent locations can be calculated. When the IoU is less than a set threshold, it indicates a significant change in the cross-section at these two locations, and a dividing line is then drawn between them. (Combined with...) Figure 2 Since the conduction paths handled by cross-sections 1 and 2 are not aligned, the change in conduction path direction can be ignored. The extension direction of the conduction path can be considered a virtual direction, and all three cross-sections can be projected onto a plane perpendicular to this virtual direction before calculating the intersection-to-union ratio. In this method, the intersection-to-union ratio of cross-sections 1 and 2 is still relatively large, so no boundary line needs to be defined. Ultimately, only the following is determined: Figure 2 The dividing line shown by the red dashed line is precisely the dividing line between the pier cap and the pier body.

[0039] It should be noted that although the final determined boundary line is precisely the boundary line between the abutment and the pier, the above method does not rely on prior structural information such as the abutment and pier (i.e., the method in this embodiment can still be executed even when it is not known in advance that the bridge pier includes pile foundations, abutments, and piers). Instead, it automatically divides the components by the change of the structural cross-section along the transmission path. This can both identify the changes in dynamic response between adjacent components (i.e., no missing components) and ensure that the dynamic response characteristics within the same component are basically consistent (i.e., no extra components are divided). In practical applications, if the abutment and pier contain different cross-sectional shapes, more components will be divided, achieving a more refined expression of dynamic response characteristics.

[0040] After the components along the conduction path are defined, for the components at both ends of the conduction path, since they may be connected to external structures and thus affected by the dynamic characteristics of those external structures, additional components and boundary conditions need to be added based on their external connections. For ease of distinction and description, this embodiment refers to the components along the conduction path as main components and the additional components to be added as boundary components. All these components will be included in the subsequent dynamic modeling scope.

[0041] Specifically, in this embodiment, the main components at both ends of the transmission path are a foundation and a pier. Therefore, a boundary element needs to be added at the bottom of the foundation and a boundary element also needs to be added at the top of the pier. The boundary element is directly connected to the boundary conditions. Therefore, the boundary element can be understood as a virtual element, which is the general term for all actual structures between the transmission path and the actual boundary conditions, used to reflect the dynamic influence of structures outside the transmission path on the main components. The boundary element only needs to ensure that the dynamic influence conforms to the actual dynamic influence, and how closely the boundary element itself conforms to the actual structure can be ignored in this application.

[0042] Optional, combined Figure 2 The boundary element connected to the bottom of the pier cap is the pile foundation, and the boundary condition connected to the pile foundation is the consolidated boundary (i.e., ground fixation) at the base of the pile foundation; the boundary element connected to the pier body is the beam and other structures on the beam, collectively referred to as the pier top superstructure, and the boundary condition connected to the pier top superstructure is the free boundary.

[0043] At this point, all components (including main components and boundary components) and boundary conditions have been determined, and dynamic response modeling can begin. This embodiment prioritizes constructing a modeling path that covers all components and boundary conditions with the fewest bifurcations, serving as the basis for subsequent dynamic state transfer. The modeling path needs to include at least one input and at least one output; in the absence of bifurcations, the number of inputs and outputs can be one. Optionally, to extend the impact force transfer process within the modeling path, this embodiment uses the consolidated boundary closer to the impact location as the input for dynamic state transfer; and the free boundary farther from the impact location as the output; thus establishing a modeling path for dynamic state transfer that covers all components and boundary conditions from the input to the output, with the fewest bifurcations. Figure 3 As shown by the black dashed arrow, the modeling path sequentially passes through the consolidated boundary, pile foundation, pile cap, pier body, superstructure at the pier top, and free boundary. Using the boundary closer to the impact location as the input allows for a longer transmission process of the impact force within the modeling path, which is beneficial for accurately representing the impact force's effect on the structure and improving modeling accuracy.

[0044] It should be noted that the modeling path here is not entirely the same as the impact force transmission path in S120. The transmission path refers to the actual transmission path of external forces in the structure. In this embodiment, the transmission path is used to determine the structures that have the most direct impact on the dynamic response location of interest (i.e., pier top displacement), and the dynamic response process inside these structures cannot be ignored. The modeling path, on the other hand, is a virtual path (or mathematical transmission path) used in the subsequent dynamic state transmission modeling. Its role in the modeling process is to provide input and output ends and establish the main transmission equation between the input and output ends. The modeling path may not be consistent with the actual force transmission path, but the response of each position in the modeling path under the action of the actual force can be mathematically balanced through the main transmission equation (for example, the actual direction of force transmission is from bottom to top, but if the upper end is the input end and the lower end is the output end, a transmission equation from the upper end to the lower end can still be established, only requiring a transformation of the transmission matrix; this process can be understood in conjunction with the operations in the subsequent steps). Therefore, in this embodiment, the transmission path and the modeling path should be distinguished. The modeling path must cover all main elements, boundary elements, and boundary conditions in order to perform the subsequent calculation of the transmission equation.

[0045] S130. Determine the dynamic response type of each main component based on its dimensions along the modeling path, the ship's impact direction, and another direction perpendicular to the modeling path and the ship's impact direction; determine the dynamic response type of each boundary component based on its position, structure, and connection with the boundary conditions.

[0046] This step determines the dynamic response type of each component. Different dynamic response types will correspond to different modeling equations in subsequent operations. For the main components, in order to accurately extract their dominant dynamic response characteristics, this embodiment abandons the limitation of simply relying on the inherent properties of materials. Instead, it scientifically defines the dynamic response type of each main component based on the principles of structural dynamics, according to the spatial geometric proportions (slenderness ratio) and relative stiffness characteristics of each component.

[0047] Optionally, this embodiment establishes a three-dimensional orthogonal coordinate system, with the three orthogonal coordinate axes pointing to the modeling path direction, the ship impact direction, and a third direction perpendicular to both the modeling path direction and the ship impact direction. Therefore:

[0048] On the one hand, if the geometric dimensions of a main component in the three orthogonal directions are of the same order of magnitude, for example, the difference in dimensions between any two directions is less than a set proportional threshold (e.g., the difference in dimensions between any two directions is less than 5% of the dimensions in those two directions), then the dynamic response type of the main component can be determined as a spatial vibrating rigid body. Specifically, when the dimensions in the three directions are relatively close, it indicates that the main component is a block or deep structure. In bridge engineering, such components have extremely high bending and shear stiffness due to their huge cross-sectional dimensions. In the dynamic system response, the elastic deformation generated inside is negligible compared to the spatial displacement of the entire system and can be directly ignored. Therefore, the dynamic behavior of this component mainly manifests as the overall six-degree-of-freedom translation and rotation in space, which can be reasonably equivalent to a spatial vibrating rigid body in dynamic response modeling. The pier in this embodiment conforms to this mechanical characteristic, so it is simplified as a spatial vibrating rigid body model.

[0049] On the other hand, if a main component has a dimension significantly larger in one of the three orthogonal directions than in the other two, its dynamic response type can be determined as a spatial vibration beam. Specifically, this geometric feature indicates that the component is a slender rod. Due to the large slenderness ratio effect, the component exhibits significant structural flexibility in the longitudinal direction. Under dynamic loads, in addition to macroscopic overall displacement, it also experiences non-negligible elastic deformations such as bending and shearing. Therefore, in dynamic response modeling, it can be equivalent to a spatial vibration beam considering the internal deformation distribution. The pier in this embodiment satisfies this characteristic, and the longitudinal axis of the pier coincides with the modeling path, so the subsequent transfer equations can be directly constructed along this axis. Optionally, the significant difference in the above dimensions can be quantified by setting a slenderness ratio (or length-to-width ratio) threshold; according to the definition of a beam in classical structural mechanics, this ratio is usually set to not less than 10 (i.e., the length is 10 times the width).

[0050] For boundary elements, the core of the dynamic modeling in this embodiment lies in accurately simulating their external influence on the main structure (i.e., the main elements), without delving into the details of internal stress transmission and local deformation. To achieve this goal, this embodiment fully examines the spatial topological location, structural characteristics, and connection with boundary conditions of each boundary element, and accordingly reasonably equates them to specific dynamic response types:

[0051] On the one hand, if the boundary element is located at the top of the entire main structure and connected to the free boundary, its dynamic response type can be defined as a spatial concentrated mass based on the primary and secondary mechanical effects of the top boundary element on the lower structure. This determination considers both the spatial topological location of the boundary element (i.e., above the main structure formed by all main elements) and the type of boundary conditions it connects to (i.e., free boundaries). The pier top superstructure in this embodiment satisfies this condition. The following explanation uses the pier top superstructure as an example to illustrate the criteria for determining the dynamic response type of this type of top boundary element. Specifically, the pier top superstructure is suspended above the pier, and its core role in the dynamic system is to transmit enormous gravity loads and dynamic inertial forces to the lower main structure. Since the top of this element is not subject to any external consolidation constraints, and the core objective of modeling is to analyze the dynamic response of the lower pier, the geometry and internal elastic deformation of the superstructure itself have a secondary impact on the dynamics of the lower main structure. Based on this primary and secondary mechanical relationship, this embodiment equates the top boundary element to a pure concentrated mass point, which contains only specific translational mass and rotational inertia. This approach not only accurately reflects the inertial loading effect of the superstructure on the piers, but also significantly reduces unnecessary system degrees of freedom.

[0052] On the other hand, if the boundary element is located at the bottom of the main structure and connected to the foundation boundary, the dynamic response type of the bottom boundary element can be determined as a spatial elastic element by decoupling its mass inertia and equivalencing its structural stiffness. This determination also considers the spatial topological location of the boundary element (i.e., located below the main structure composed of all main elements), the type of boundary conditions connected to the boundary element (i.e., consolidated boundary), and the structural characteristics of the boundary element itself (i.e., the structural stiffness equivalence mentioned below). In this embodiment, the pile foundation deeply anchored in the ground satisfies this condition. The following uses the pile foundation as an example to explain the basis for determining the dynamic response type of this type of bottom boundary element. Specifically, the dynamic response type of the pile needs to comprehensively consider two dimensions of mechanical characteristics: the first dimension is the decoupling of mass inertia. Because the pile foundation is deeply buried in the soil layer, it has a close friction and embedding effect with the surrounding soil. This strong foundation constraint causes the dynamic inertial force of the pile foundation itself to be largely absorbed and restricted by the surrounding soil layer, thereby greatly weakening the direct influence of its mass on the dynamic displacement of the upper abutment and pier. Therefore, when determining its dynamic response type, the mass properties of the pile foundation itself can be reasonably ignored. The second dimension is the equivalence of structural stiffness. Under external dynamic loads, the system of pile-soil interaction exhibits extremely significant elastic resistance characteristics. This spatial constraint capability is key to maintaining the stability of the main structure above. Combining the neglect of mass inertia and the retention of elastic constraints, this embodiment ultimately equates the bottom boundary element as a spatial elastic hinge. This dynamic response type, by extracting a six-degree-of-freedom elastic constraint matrix with specific stiffness coefficients, can accurately simulate the spatial translational and rotational constraint effects exerted on the pile cap by the entire pile-soil system, improving the solution efficiency of the overall dynamic response equation while ensuring the authenticity of the physical boundary conditions.

[0053] The above two aspects provide two methods for determining the type of dynamic response. Further extending the second method, we can conclude that if a boundary element simultaneously satisfies the two core conditions of mass-inertia decoupling and providing spatial resistance during dynamic transmission, its dynamic response type can be determined as a spatial elastic hinge. The lower pile foundation in this embodiment belongs to this typical working condition. By ignoring its dynamic mass constrained by the soil layer and extracting its spatial stiffness matrix, it is ultimately equivalent to a spatial elastic hinge, thus scientifically and realistically reflecting the six-degree-of-freedom elastic constraint of the pile foundation on the pile cap. This extended method is also applicable to other working conditions; as long as the element satisfies the above two core conditions, its dynamic response type can be determined as a spatial elastic hinge.

[0054] In summary, this embodiment provides a method for classifying modeling elements and determining their dynamic response types based on spatial geometric scale characteristics through steps S120 and S130. This method closely matches the macroscopic mechanical characteristics of large-scale civil engineering structures such as bridges. In the field of civil engineering, structural components have large absolute dimensions, and there are significant differences in relative stiffness between components, such as deep foundations and slender piers. However, this method is not entirely applicable to engineering fields such as precision machinery or aerospace, which operate under complex high-frequency excitation environments. This is because, under such conditions, even small blocks cannot ignore the internal stress wave transmission and local elastic deformation. Therefore, this method, which discards microscopic material differences and directly utilizes macroscopic geometric scale and relative stiffness differences to classify components, is a core innovation of this invention based on the dynamic characteristics of large-scale engineering structures.

[0055] Of course, besides the methods mentioned above, other methods can also be used to determine the dynamic response types of each component. For example, based on engineering experience, bridge piers can be artificially divided into several components: pile foundation, pile cap, pier body, and superstructure at the top of the pier. The dynamic response type of the pile foundation can be artificially determined as a spatial elastic hinge, the pile cap as a spatial vibrating rigid body, the pier body as a spatial vibrating beam, and the superstructure at the top of the pier as a spatial vibrating concentrated mass, etc. After artificially determining this information, dynamic modeling can still be performed using subsequent steps. This is also a specific implementation method of this application and falls within the scope of protection of this invention.

[0056] However, compared with the method of dividing components and determining dynamic response types based on engineering experience, the advantages of the S120-S130 method are as follows: This method can automatically determine a reasonable component division method and determine a reasonable dynamic response type for each component through path analysis and dimensional analysis; when lacking engineering experience, this method can also perform reasonable structural division through data analysis alone; at the same time, this method does not rely on any prior information about the building structure, that is, when facing an unfamiliar structure, even without prior structural information such as pile foundations, abutments, piers, and beams, it can still divide the components and dynamic response types suitable for subsequent dynamic modeling through data analysis, which is more generalizable.

[0057] S140. Based on the dynamic response type of each component, construct the transfer equations of the dynamic state of each component and the dynamic equations under ship impact.

[0058] Once the components and their dynamic response types are determined, the bridge collision can be transformed into... Figure 4The dynamic model shown in the model is as follows: 1 is a spatial elastic hinge (used to characterize the constraint effect of the pile foundation on the cap), 2 is a spatial vibration rigid body (cap) with one end input and one end output, 3 is a spatial vibration beam (pier body, specifically considering longitudinal vibration of the x-axis, torsional vibration around the x-axis, and transverse vibration of the y-axis and z-axis Euler-Bernoulli beam), 4 is a spatial vibration concentrated mass (superstructure of the pier top), 0 is the ground number (consolidated boundary), and 5 is the free boundary number.

[0059] Based on the above model, dynamic response modeling and pier response can be performed. Specifically, dynamic response modeling requires the construction of two types of equations: one is the transfer equation of the dynamic state (referred to as the transfer equation), which is used to characterize the transfer relationship of the dynamic state in the system. In this embodiment, this equation will be used to solve for the natural frequencies and mode shapes (also called characteristic vectors) of the structure under each vibration mode; the other is the dynamic equation, which is used to characterize the relationship between force and motion in the system. In this embodiment, this type of equation will be used to solve for the generalized coordinates of each mode shape of the structure. Finally, using each mode shape and its generalized coordinates, the dynamic response of the pier can be synthesized.

[0060] Therefore, this step first constructs the transfer equations of the dynamic state of each component according to different dynamic response types. In a specific embodiment, the following dynamic state transfer equations can be constructed for pile foundations, pile caps, and piers:

[0061] (1)

[0062] (2)

[0063] in, This represents the state vector (i.e., dynamic state) at the input end. The output state vector (i.e., dynamic state) represents the input of each component, which is the bottom of the component, and the output is the top of the component. For the transfer matrix, These represent translational displacements along the x, y, and z axes, respectively. These represent the forces acting along the x, y, and z axes, respectively. These represent rotational displacements about the x, y, and z axes, respectively. These represent the torques about the x, y, and z axes, respectively. The x-axis points in the direction of the modeling path, the y-axis points in the direction of the ship's impact, and the z-axis points in a direction perpendicular to both the x and y axes.

[0064] It should be noted that in the transfer equations for different components, the meaning of each variable is specific to the current component. For example, in the transfer equations for pile foundations, This represents the state vector at the input end of the pile foundation. This represents the state vector at the output end of the pile foundation. The transfer matrix for pile foundations; in middle, These represent the translational displacements of the pile foundation input end along the x, y, and z axes, respectively. These represent the forces acting on the input end of the pile foundation along the x, y, and z axes, respectively. These represent the rotational displacements of the pile foundation input end about the x, y, and z axes, respectively. These represent the moments about the x, y, and z axes at the pile input end, respectively; middle, These represent the translational displacements of the pile foundation's output end along the x, y, and z axes, respectively. These represent the forces acting on the output end of the pile foundation along the x, y, and z axes, respectively. These represent the rotational displacements of the pile foundation's output end about the x, y, and z axes, respectively. These represent the torques at the pile foundation output end about the x, y, and z axes, respectively. Other components are similar and will not be described further.

[0065] For the superstructure at the pier top, the following dynamic state transfer equations can be constructed:

[0066] (3)

[0067] (4)

[0068] The meanings of the variables are the same as in equations (1) and (2). The difference is that, since the superstructure at the pier top has no dimensions, components such as torque and rotational displacement are removed from the state vector. Furthermore, for the pile foundation, pile cap, pier body, and superstructure at the pier top, due to their different dynamic response types, their transfer matrices... The specific elements also differ. The transfer matrices differ for elements with different dynamic response types; their specific elements and calculation methods can be found in the literature. To facilitate understanding of this application, this embodiment exemplarily demonstrates the transfer matrices of a spatial elastic hinge and a spatial vibrating beam:

[0069] Specifically, the transfer matrix of the spatial elastic hinge is:

[0070] (1)

[0071] (2)

[0072] in, O represents the identity matrix. , , These represent the stiffness of the linear springs along the x, y, and z axes (i.e., the stiffness of the pile foundation along the three directions). , , These represent the stiffness of the torsional springs in the three directions (the torsional stiffness of the pile foundation in the three directions). The specific values ​​of each stiffness can be obtained through finite element analysis, such as static analysis software.

[0073] The transfer matrix of the spatially vibrating beam is:

[0074] (3)

[0075] In the formula:

[0076] (8)

[0077] (9)

[0078] in, , , , For Krylov functions, the Krylov function contains It is an independent variable that applies only to the function itself; Right now ,express Figure 4 The length of the spatially vibrating beam 3 along the beam body direction; Indicates the axial wave number. Indicates the elastic modulus. This represents the cross-sectional area of ​​the beam. Indicates the torsional wave number. Indicates the shear modulus. The polar moment of inertia of the beam section is represented by the subscript. The pier body is numbered 3. Represents the bending wave number in the xy plane. Represents the bending wave number in the xz plane. This represents the moment of inertia of the beam section about the z-axis. This represents the moment of inertia of the beam section about the y-axis. This represents the mass per unit length of the beam. This indicates the density of concrete. Indicates the length of the beam. It represents the vibration frequency (i.e., the natural frequency) of the structure.

[0079] Simultaneously, this step constructs the dynamic equations for each component based on its dynamic response type. In one specific embodiment, since the spatial elastic hinge is massless, the following dynamic equations can be constructed for the pier cap, pier body, and pier top superstructure, respectively:

[0080] (10)

[0081] In the formula, , , , For components The parameter matrix; Characteristic elements The mass distribution of is called the mass parameter matrix; Representation element The motion state of a body is a matrix composed of the displacement (translational displacement + rotational displacement) variables of the body element, which is called the displacement matrix of the element. Acting on Indicator element The internal forces, excluding damping forces, and their locations of action are called the stiffness parameter matrix. For components The external forces (including external torques) acting on the object are arrayed, i.e., impact forces.

[0082] Furthermore, for pile foundations, pile caps, pier bodies, and pier top superstructures, due to their different types of dynamic response, their... , , , The specific elements also differ. The parameter matrices of elements with different dynamic response types can be found in the literature. To facilitate understanding of this application, this embodiment exemplarily demonstrates a spatial vibration beam ( The parameter matrix of (=3):

[0083] (11)

[0084] (12)

[0085] in, This represents the distributed line load (distributed axial force) along the x-axis, i.e., the axial force per unit length. This represents the distributed line load (distributed transverse force) along the y-axis, i.e., the y-direction shear force per unit length. This represents the distributed line load (distributed lateral force) along the z-axis. This represents the distributed torque about the x-axis, that is, the torsional torque per unit length. Indicates the position along the length of the beam.

[0086] S150. Sequentially assemble the transfer equations of each component along the modeling path to obtain the overall transfer equation of the pier; determine the characteristic vectors of each component under each vibration mode based on the overall transfer equation of the pier; sequentially assemble the characteristic vectors of each component along the modeling path to obtain the augmented characteristic vectors of the pier under each vibration mode.

[0087] This embodiment uses the transfer equation to solve for the augmented characteristic vector of the bridge pier under various vibration modes. In one specific implementation, the process may include the following steps:

[0088] Step 1: Concatenate the transfer equations of each component sequentially along the modeling path to obtain the overall transfer equation of the pier. This step, based on the transfer equations of each component, concatenates to obtain the overall transfer equation of the pier, eliminating the need to model the complex transfer equation of the entire pier. Optionally, along the modeling path, the transfer matrices in the transfer equations of the pile foundation, pile cap, pier body, and pier top superstructure can be processed. , , , By piecing them together, we obtain the overall transfer equation for the bridge piers:

[0089] (13)

[0090]

[0091] in, This represents the total transfer matrix of the bridge piers. According to the rules of matrix multiplication, it is necessary to... Expand to a 12×12 matrix. Describe the boundary conditions of the bridge piers:

[0092] (14)

[0093]

[0094] in, The state vector representing the free boundary (that is, the output of the concentrated mass 4 in spatial vibration). This represents the state vector of the consolidation boundary (which is the input of the spatial elastic hinge 1).

[0095] Step 2: Determine the characteristic vectors of each component under each vibration mode based on the overall transfer equation of the pier. Optionally, the characteristic equation of the pier can be obtained first from the overall transfer equation (13):

[0096] (15)

[0097] In this embodiment, After removing the zero element, it is denoted as ,Will Remove and The square matrix obtained after the columns corresponding to the zero elements is denoted as . .

[0098] Then, by solving the characteristic equation (15), the natural frequencies of the bridge pier under each vibration mode can be obtained, respectively. ( =1,2,……, indicating the first, second,…… (Vibration modes). Each mode has its own natural frequency, and the natural frequencies of each component are the same as the natural frequencies of the entire pier.

[0099] Finally, the natural frequencies of each vibration mode are substituted sequentially into the transfer equations of the pile foundation, pile cap, pier body, and pier top superstructure to solve for the characteristic vectors of each vibration mode. Optionally, this process may include steps S1-S2:

[0100] S1. Substituting the natural frequencies of each vibration mode into the overall transfer equation of the pier, the boundary conditions of the pier under each vibration mode can be obtained respectively. Then, the boundary conditions of the pier under each vibration mode are substituted into the transfer equation of the pile foundation, and transferred sequentially through the transfer equations of the pile cap, pier body, and pier top superstructure to obtain the state vectors of the pile cap, pier body, and pier top superstructure under each vibration mode.

[0101] Optionally, respectively Substituting into the overall transfer equation (13), we can obtain the total number of bridge piers at each... The state vector at the lower input terminal ; through the transfer equation , , , This allows us to further obtain the state vector of any point within the system (i.e., the entire bridge pier). This represents the state vector at the boundary between the pile foundation and the pile cap. This represents the state vector at the boundary between the pier cap and the pier body. Indicates any position of the pier body The state vector at that location. Where, each time... When substituting into the transfer equation, This is equivalent to the natural frequency in the transfer equation. For example, When substituting into the transfer equation of the pier body, This is equivalent to the natural frequency in equation (8). Thus, the corresponding state vector can be solved.

[0102] S2. Extract displacement components from the state vectors of the pier cap, pier body, and pier top superstructure under each vibration mode, and collectively construct the characteristic vectors of the pier cap, pier body, and pier top superstructure under each vibration mode:

[0103] (16)

[0104] in, , , These respectively represent the pile cap, pier body, and pier top superstructure in the [number]th [year]. eigenvectors of vibration modes , , transpose, These represent the points at the junction of the pile foundation and the pile cap. Displacement along the x, y, z axes under the first vibration mode. These represent the points at the junction of the pile foundation and the pile cap. Rotational displacement about the x, y, z axes under the first vibration mode. These represent the continuous positions of the pier body. At the Displacement along the x, y, z axes under the first vibration mode. Indicates the continuous position of the pier body At the Rotational displacement about the x-axis under the first vibration mode. They respectively indicate that the upper part of the pier body and the top of the pier are sufficient for the first Displacement along the x, y, z axes under the first vibration mode.

[0105] Step 3: Sequentially splice the feature vectors of each component along the modeling path to obtain the augmented feature vectors of the pier under each vibration mode. Optionally, the pier cap, pier body, and pier top superstructure are sequentially spliced ​​along the modeling path in the [missing information - likely a specific step or step]. eigenvectors of vibration modes , , The bridge pier was obtained at the first Augmented eigenvectors under first vibration modes :

[0106] (17)

[0107] Among them, the characteristic vector of the pier body is continuous, the elements of the characteristic vector of a discrete system are all discrete variables, and the elements of the characteristic vector of a continuous system are all continuous functions. The augmented characteristic vector of a multi-rigid-flexible body system containing both discrete and continuous elements includes elements of both discrete variables describing the discrete elements and continuous functions describing the continuous elements. Therefore, the augmented characteristic vector of the system has 9 discrete quantities and 4 continuous functions (based on the length along the beam extension direction). (As the degree of continuity of the variables), the first 6 discrete quantities describe the motion of the spatially vibrating rigid body 2 (pillar), the 4 continuous functions describe the motion of the spatially vibrating beam (pier), and the remaining 3 discrete quantities describe the motion of the spatially vibrating concentrated mass.

[0108] S160. The dynamic equations of each component are sequentially assembled along the modeling path to obtain the dynamic equation of the pier. Based on the dynamic equation of the pier, the generalized coordinates of the pier under each mode are calculated. Based on the augmented characteristic vector and generalized coordinates of the pier under each mode, the dynamic response of the pier is calculated.

[0109] This step will augment the feature vector. Substituting the dynamic equations of the system into the equations, and using the orthogonality of the augmented vectors and modal analysis, the decoupled system motion differential equations are obtained. The generalized coordinates of the system are obtained by integrating the motion differential equations using numerical analysis. Finally, the structural dynamic response is obtained based on the correspondence between the generalized coordinates and the physical coordinates.

[0110] In one specific embodiment, the process may include the following steps:

[0111] Step 1: Sequentially assemble the dynamic equations of each component along the modeling path to obtain the dynamic equation of the pier. This step, based on the dynamic equations of each component, assembles the overall dynamic equation of the pier, eliminating the need for complex modeling of the overall dynamic equation of the pier. Optionally, if the spatial elastic hinge is massless, the overall dynamic equation of the pier is obtained by assembling the dynamic equations of components 2, 3, and 4:

[0112] (18)

[0113] in, These represent the mass parameter matrix, stiffness parameter matrix, displacement matrix, and external force matrix of the bridge pier, respectively.

[0114] (19)

[0115] in, These represent the mass parameter matrix, stiffness parameter matrix, displacement matrix, and external force matrix of the foundation, respectively. These represent the mass parameter matrix, stiffness parameter matrix, displacement matrix, and external force matrix of the pier body, respectively. These represent the mass parameter matrix, stiffness parameter matrix, displacement array, and external force array of the superstructure at the pier top, respectively.

[0116] Optionally, the input impact force time history can be determined based on the ship's speed, tonnage, and other parameters using existing simplified impact force time history calculation methods, according to the ship type provided in the AASHTO standard. ; and Then it is 0.

[0117] Step 2: Calculate the generalized coordinates of the pier under each mode based on the pier's dynamic equations. Specifically, using modal analysis, this embodiment calculates the displacement matrix of the pier to be solved. This can be represented as a decomposition into:

[0118] (20)

[0119] in, Represents the augmented eigenvector The corresponding generalized coordinates have already been obtained in S140. This step will then solve the dynamic equations based on the bridge piers. .

[0120] Optionally, substituting equation (20) into equation (18) yields:

[0121] (twenty one)

[0122] Then, using augmented feature vectors Taking the inner product of both sides of equation (21) and utilizing the orthogonality of the augmented eigenvectors, we can obtain:

[0123] (twenty two)

[0124] in, Represents the p-th order modal mass. denoted by , where represents the natural frequency of the p-th mode and n represents the mode order.

[0125] Finally, by integrating equation (22) along each time step using numerical integration, the generalized coordinates can be solved. .

[0126] Step 3: Calculate the dynamic response of the bridge piers based on the augmented feature vectors and generalized coordinates. Optionally, the generalized coordinates... Substitute into equation (20) to solve. This refers to the dynamic response of the bridge pier, which includes the displacement at the pier top. The calculation details not covered in steps two and three are existing technologies and will not be elaborated here.

[0127] The entire process described above can also be combined Figure 5 Please refer to the flowchart shown for comprehension. Figure 5 The bridge pier dynamics model in the text refers to... Figure 4 The structural model shown Figure 5 All the solution steps (mainly corresponding to S140 and S150) together constitute the prediction model of the dynamic response of the bridge pier under ship impact in this embodiment. The model reflects the spatial action mechanism of the bridge pile foundation through the transfer equation and dynamic equation, so that the dynamic response of the bridge pier under ship impact can be obtained through a small number of equation calculations, which has a faster prediction speed than numerical simulation.

[0128] In summary, this embodiment proposes a method for constructing a rapid predictive model of the dynamic response of bridge piers under ship impact. This method first discretizes the complex bridge pier system into multiple modeling elements through path analysis and dimensional analysis. Then, based on the significant differences in macroscopic scale and stiffness of bridge engineering, the dynamic response type of each modeling element is determined. Next, frequency characteristic equations are established using the state vector transfer matrix between elements and system boundary conditions to obtain the natural frequencies of the bridge pier and the characteristic vectors of each element. Based on this, the ship impact force time history is introduced as an external excitation to construct the dynamic response equations of the entire bridge pier system. Finally, the characteristic vectors of each element are extracted to construct an augmented feature space. Coordinate transformation is used to convert the originally coupled physical space dynamic equations into independent modal equations for solving, ultimately obtaining the accurate dynamic response process of the bridge pier in the time domain. Based on the above process, the method of this embodiment can achieve the following beneficial effects:

[0129] 1. The method in this embodiment addresses the current situation where the dynamic response of ship-bridge collisions mainly relies on numerical simulation technology. Based on the dynamic state transfer equation and dynamic equation, a novel dynamic response prediction model is proposed. This model can quickly predict the dynamic response of ship-bridge collisions with a small number of equations, thus solving the shortcomings of large computational load and slow prediction speed in numerical simulation.

[0130] 2. The method in this embodiment fully considers the spatial geometric features of the structure in the modeling process, taking into account the rotation, bending and vibration of the structure in space. Compared with the simplified planar structure in traditional theory, it is more in line with the actual situation and can better describe the dynamic response characteristics of the structure under ship impact.

[0131] 3. The method in this embodiment does not require the establishment of the overall dynamic equation of the pier. The overall transfer matrix and dynamic equation of the pier can be obtained by assembling the transfer matrix and dynamic equation of the individual components. The dynamic response modeling is more flexible, and the matrix order of the chain system depends on the order of the component transfer matrix, resulting in higher solution efficiency.

[0132] 4. The method in this embodiment provides a way to divide modeling elements according to structural dimensions and determine the dynamic response type of each element. It is applicable to civil engineering structures such as bridges that have significant differences in macroscopic scale and stiffness. This method automatically determines a reasonable element division method and a reasonable dynamic response type for each element through path analysis and dimensional analysis. It does not rely on engineering experience or prior structural information, thus improving the automation of modeling and facilitating the realization of the bridge pier dynamic response prediction in this embodiment.

[0133] It should be noted that all data involved in this application are information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with the relevant laws, regulations and standards of the relevant countries and regions, and corresponding operation portals are provided for users to choose to authorize or refuse.

[0134] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention, such as... Figure 6 As shown, the device includes a processor 60, a memory 61, an input device 62, and an output device 63; the number of processors 60 in the device can be one or more. Figure 6 Taking a processor 60 as an example; the processor 60, memory 61, input device 62, and output device 63 in the device can be connected via a bus or other means. Figure 6 Taking the example of a connection between China and Israel via a bus.

[0135] The memory 61, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules, such as the program instructions / modules corresponding to the method for constructing a prediction model of the dynamic response of a bridge pier under ship impact in this embodiment of the invention. The processor 60 executes various functional applications and data processing of the device by running the software programs, instructions, and modules stored in the memory 61, thereby realizing the above-mentioned method for constructing a prediction model of the dynamic response of a bridge pier under ship impact.

[0136] The memory 61 may primarily include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on terminal usage. Furthermore, the memory 61 may include high-speed random access memory and non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, the memory 61 may further include memory remotely located relative to the processor 60, and these remote memories can be connected to the device via a network. Embodiments of the aforementioned network include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0137] Input device 62 can be used to receive input digital or character information, and to generate key signal inputs related to user settings and function control of the device. Output device 63 may include display devices such as a display screen.

[0138] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for constructing a prediction model of the dynamic response of a bridge pier under ship impact according to any embodiment.

[0139] The computer storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0140] Computer-readable signal media may include ship data signals in baseband or as part of a carrier wave, carrying computer-readable program code. Such ship data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which may transmit, ship, or transport programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0141] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0142] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as C or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a predictive model of the dynamic response of a bridge pier under ship impact, characterized in that, include: Obtain the impact location of the ship on the bridge pier, and the location of the dynamic response to be predicted; Along the transmission path of the impact force from the impact location to the response location, compare the cross-sections of the pier structure, draw a dividing line at the point where the cross-section changes, and divide the pier structure through which the transmission path passes into multiple main elements; according to the external connection of the main elements at both ends of the transmission path, add boundary elements and boundary conditions; based on each element and boundary condition, construct the modeling path with the fewest bifurcations. Based on the dimensions of each main component along the modeling path, the ship's impact direction, and another direction perpendicular to the modeling path and the ship's impact direction, determine the dynamic response type of each main component; based on the position, structure, and connection of each boundary component with the boundary conditions, determine the dynamic response type of each boundary component. Based on the dynamic response type of each component, the transfer equations of the dynamic state of each component and the dynamic equations under ship impact are constructed respectively. The transfer equations of each component are sequentially assembled along the modeling path to obtain the overall transfer equation of the pier; based on the overall transfer equation of the pier, the characteristic vectors of each component under each vibration mode are determined; the characteristic vectors of each component are sequentially assembled along the modeling path to obtain the augmented characteristic vectors of the pier under each vibration mode. The dynamic equations of each component are sequentially assembled along the modeling path to obtain the dynamic equation of the pier. Based on the dynamic equation of the pier, the generalized coordinates of the pier under each mode are calculated, and the dynamic response of the pier is calculated based on each augmented characteristic vector and the generalized coordinates.

2. The method according to claim 1, characterized in that, The impact location is the pile cap, and the response location to be predicted is the pier top; each main component includes the pile cap and the pier body, and each boundary component includes the pile foundation and the superstructure at the pier top; each boundary condition includes the consolidated boundary at the base of the pile foundation and the free boundary at the top of the superstructure at the pier top. Accordingly, constructing the modeling path with the fewest branching points based on each component and boundary condition includes: The consolidated boundary closer to the impact point is used as the input end for dynamic state transmission; the free boundary farther from the impact point is used as the output end for dynamic state transmission. Establish a path from the input end to the output end that covers all components and boundary conditions and has the fewest branching points as the modeling path for dynamic state transmission. The modeling path passes through the consolidated boundary, pile foundation, pile cap, pier body, pier top superstructure, and free boundary in sequence.

3. The method according to claim 1, characterized in that, The determination of the dynamic response type of each main component based on its dimensions along the modeling path, the ship's impact direction, and another direction perpendicular to the modeling path and the ship's impact direction includes: If the difference between any two dimensions of the main component along the modeling path, along the ship impact direction, and along another direction perpendicular to the modeling path and the ship impact direction is less than a set ratio, the dynamic response type of the main component is determined to be a spatial vibrating rigid body. If the ratio of the size of the main component along the modeling path to its size along the ship's impact direction, and the ratio of the size of the main component along the modeling path to its size along another direction perpendicular to both the modeling path and the ship's impact direction, are both greater than a set multiple, then the dynamic response model of the main component is determined to be a spatial vibration beam.

4. The method according to claim 1, characterized in that, The determination of the dynamic response type of each boundary element based on its position, structure, and connection with the boundary conditions includes: If the top boundary element is connected to the free boundary, the dynamic response type of the top main element is determined to be a sizeless spatial vibration concentrated mass based on the primary and secondary mechanical effects of the top boundary element on the lower structure. If the bottom boundary element is connected to the solidified boundary, by decoupling the mass inertia and equivalencing the structural stiffness of the bottom boundary element, the dynamic response type of the bottom boundary element is determined to be a massless spatial elastic element.

5. The method according to claim 1, characterized in that, Each main component includes the pile cap and the pier body, and each boundary component includes the pile foundation and the superstructure on the pier top; the dynamic response type of the pile foundation is a spatial elastic hinge, the dynamic response type of the pile cap is a spatial vibrating rigid body, the dynamic response type of the pier body is a spatial vibrating beam, and the dynamic response type of the superstructure on the pier top is a spatial vibrating concentrated mass. Accordingly, based on the dynamic response type of each component, the transfer equations of the dynamic state of each component and the dynamic equations under ship impact are constructed respectively, including: For pile foundations, pile caps, and piers, the following dynamic state transfer equations are constructed respectively: For the superstructure at the pier top, the following dynamic state transfer equations are constructed: in, This represents the state vector at the input terminal. This represents the state vector at the output terminal. For the transfer matrix of the component, These represent translational displacements along the x, y, and z axes, respectively. These represent the forces acting along the x, y, and z axes, respectively. These represent rotational displacements about the x, y, and z axes, respectively. These represent the torques about the x, y, and z axes, respectively. The x-axis points in the direction of the modeling path, the y-axis points in the direction of the ship's impact, and the z-axis points in a direction perpendicular to both the x and y axes. For the pier cap, pier body, and pier top superstructure, the following dynamic equations are constructed respectively: in, , , , These represent the mass parameter matrix, stiffness parameter matrix, displacement matrix, and external force matrix of the components, respectively; the external force matrix of the foundation is the ship impact force, while the external force matrices of the other components are 0; the displacement matrix of each component... From the state vector or The translational and rotational displacement components are represented in the matrix. The displacement arrays of the pier cap and the superstructure of the pier top are discrete variable arrays, while the displacement array of the pier body is a continuous variable array.

6. The method according to claim 1, characterized in that, The modeling path sequentially passes through the consolidated boundary of the pile base, the pile foundation, the pile cap, the pier body, the superstructure of the pier top, and the free boundary at the top of the superstructure of the pier top. Accordingly, the transfer equations of each component are sequentially assembled along the modeling path to obtain the overall transfer equation of the bridge pier, including: Along the modeling path, the transfer matrix in the transfer equations for the pile foundation, pile cap, pier body, and pier top superstructure is... , , , By piecing them together, we obtain the overall transfer equation for the bridge piers: in, Represents the overall transfer matrix of the bridge piers. Describe the boundary conditions of the bridge piers: in, The state vector representing the free boundary. The state vector representing the consolidation boundary. These represent translational displacements along the x, y, and z axes, respectively. These represent the forces acting along the x, y, and z axes, respectively. These represent rotational displacements about the x, y, and z axes, respectively. These represent the torques about the x, y, and z axes, respectively. The x-axis points in the direction of the modeling path, the y-axis points in the direction of the ship's impact, and the z-axis points in a direction perpendicular to both the x and y axes. Accordingly, determining the characteristic vectors of each component under each vibration mode based on the overall transfer equation of the bridge pier includes: Based on the overall transfer equation of the bridge pier, the characteristic equation of the bridge pier is obtained: in, express Remove and The square matrix following the column corresponding to the zero element, where det represents the determinant of the square matrix; Solving the characteristic equation yields the natural frequencies of the bridge pier under each vibration mode. Substitute the natural frequencies of each vibration mode into the transfer equations of the pile foundation, pile cap, pier body, and pier top superstructure, and solve for the characteristic vectors of the pile foundation, pile cap, pier body, and pier top superstructure under each vibration mode.

7. The method according to claim 6, characterized in that, The process involves substituting the natural frequencies of each vibration mode into the transfer equations of the pile foundation, pile cap, pier body, and pier top superstructure, and then solving for the characteristic vectors of the pile foundation, pile cap, pier body, and pier top superstructure under each vibration mode, including: Substituting the natural frequencies of each vibration mode into the overall transfer equation of the bridge pier, the boundary conditions of the bridge pier under each vibration mode are obtained respectively. Substitute the boundary conditions of the pier under each vibration mode into the transfer equation of the pile foundation, and then transfer them sequentially through the transfer equations of the pile cap, pier body, and pier top superstructure to obtain the state vectors of the pile cap, pier body, and pier top superstructure under each vibration mode. From the state vectors of the pier cap, pier body, and pier top superstructure under each vibration mode, the characteristic vectors of the pier cap, pier body, and pier top superstructure under each vibration mode are extracted respectively: in, Indicates the modal order. , , These respectively represent the pile cap, pier body, and pier top superstructure in the [number]th [year]. eigenvectors of vibration modes , , transpose, These represent the points at the junction of the pile foundation and the pile cap. Translational displacements along the x, y, z axes under the first vibration mode. These represent the points at the junction of the pile foundation and the pile cap. Rotational displacement about the x, y, z axes under the first vibration mode. These represent the continuous positions of the pier body. At the Translational displacements along the x, y, z axes under the first vibration mode. Indicates the continuous position of the pier body At the Rotational displacement about the x-axis under the first vibration mode. These respectively indicate the points at which the pier body and the superstructure of the pier top meet. Translational displacements along the x, y, z axes under the first vibration mode; Accordingly, the augmented feature vectors of each element are sequentially spliced ​​along the modeling path to obtain the pier's feature vectors under each vibration mode, including: The foundation, pier body, and superstructure of the pier top are sequentially assembled along the modeling path in the [number]th [stage]. eigenvectors of vibration modes , , The bridge pier was obtained at the first Augmented eigenvectors under first vibration modes : 。 8. The method according to claim 1, characterized in that, The dynamic equations of the bridge piers are obtained by sequentially piecing together the dynamic equations of each component along the modeling path, including: By sequentially piecing together the dynamic equations of the abutment, pier body, and superstructure at the top of the pier along the modeling path, the dynamic equations of the bridge pier are obtained: in, These represent the mass parameter matrix, stiffness parameter matrix, displacement matrix, and external force matrix of the bridge pier, respectively. , These represent the mass parameter matrix, stiffness parameter matrix, displacement matrix, and external force matrix of the foundation, respectively. These represent the mass parameter matrix, stiffness parameter matrix, displacement matrix, and external force matrix of the pier body, respectively. These represent the mass parameter matrix, stiffness parameter matrix, displacement array, and external force array of the superstructure at the pier top, respectively.

9. The method according to claim 8, characterized in that, The calculation of the generalized coordinates of the bridge pier under each mode, and the calculation of the dynamic response of the bridge pier based on each augmented eigenvector and the generalized coordinates, includes: Modal analysis was applied to array the displacements of the bridge piers. Decomposed into: （20） in, Represents the augmented eigenvector Corresponding generalized coordinates; Substituting equation (20) into the dynamic equation of the bridge pier, we get: （21） Using augmented eigenvectors Taking the inner product of both sides of equation (21) and utilizing the orthogonality of the augmented eigenvectors, we can obtain: （22） in, Represents the p-th order modal mass. The natural frequency of the p-th mode is represented by n, and the modal order is represented by n. By integrating equation (22) using numerical integration, the generalized coordinates can be solved. ; generalized coordinates Substitute into equation (20) and solve. As a dynamic response of bridge piers.

10. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method for constructing a prediction model of the dynamic response of a bridge pier under ship impact as described in any one of claims 1-9.

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