A method for predicting the dynamic response of a nonlinear connected floating bridge considering the time-varying effect of multi-cabin flooding in waves

Abstract

The application discloses a kind of nonlinear connection through load floating bridge dynamic response prediction method considering wave in multi-cabin water inflow time-varying effect.It includes: establishing the nonlinear connection floating bridge dynamic analysis model of liquid cabin in static water, determining the balance position coordinate and inclination;Based on the potential flow theory, the additional hydrodynamic coefficient and wave excitation load transfer function database of different liquid cabin working condition and wave frequency wave direction are established;Establish the water quantity time-varying model of damaged cabin in wave, obtain the water inflow load;Water inflow load, additional hydrodynamic load, wave excitation load are substituted into time-domain hydrodynamic analysis equation, and the dynamic response of through load floating bridge under the water quantity time-varying of multiple cabin is obtained by solving.The application can accurately consider the coupling effect of wave and moving load under the coupling effect of wave and moving load, improve the prediction accuracy and efficiency.

Description

Technical Field

[0001] This invention belongs to the field of floating bridge dynamic response technology, and in particular relates to a nonlinear connected through-load floating bridge dynamic response prediction method that considers the time-varying effect of multi-compartment water ingress in waves. Background Technology

[0002] Floating bridges, as temporary or semi-permanent waterways, are widely used in rescue, transportation, and other fields. They are typically composed of multiple longitudinally connected sections, enabling rapid deployment and dismantling in complex waterways. However, in reality, floating bridges can be affected by corrosion, collisions, and impacts, leading to damage and water ingress into multiple compartments. This can alter the mechanical properties of the bridge sections, increase the load on the connectors, and reduce the structural safety, stability, and passage capacity of the floating bridge.

[0003] Currently, research on the dynamic response of floating bridges damaged by waves and flooding is relatively limited, especially the dynamic response analysis of nonlinear connected floating bridges considering the time-varying effects of multi-compartment flooding under the combined action of waves and moving loads, for which there is no existing technology. Related research mainly focuses on the dynamic response analysis of multi-floating body systems with liquid tanks. Existing research methods mainly fall into the following three categories:

[0004] (1) Time-domain hydrodynamic analysis method combining multi-rigid-body dynamics and potential flow theory: A multi-floating-body system model is established using the Lagrange method or the Newton-Euler method, and the hydrodynamic effects of the internal and external flow fields of the floating body are described by combining potential flow theory, ignoring the process of water entering and leaving the compartments. This method is based on a determined amount of liquid in the tanks to carry out multi-floating-body hydrodynamic analysis, which cannot characterize strongly nonlinear time-varying processes such as water ingress due to dam breaches, and requires additional constraint equations to be solved simultaneously to handle nonlinear connection problems.

[0005] (2) CFD-based fluid-structure interaction analysis method: By solving the governing equations (Navier-Stokes equations) of fluid motion, the interaction between the internal and external flow fields and the multi-floating body structure can be simulated, which can accurately capture the complex behavior of the fluid. However, high-precision CFD simulation of the external wave field of the floating bridge and the water inflow field inside multiple compartments is computationally very expensive, has stringent requirements on mesh quality and computational resources, and requires in-depth code development and integration when dealing with nonlinear connection problems. Therefore, this method is difficult to use for efficient prediction of the dynamic response of large-scale multi-floating body systems.

[0006] (3) Model test method based on similarity theory: Based on the dominant force, the similarity criterion is determined, and through scaled-down model tests, relatively reliable dynamic response data of multi-floating body system after hull breach can be obtained, providing a key basis for the calibration of numerical model. However, this method also has inherent limitations, including scale effect, long preparation period, high test cost, low efficiency of multi-condition test, and some local physical quantities are difficult to measure accurately and without interference.

[0007] When a floating bridge in a wave environment experiences a breach, external water rapidly floods into the damaged compartments, causing drastic changes in the buoyancy and stability of the bridge sections and a significant increase in the load on the connectors between the sections. Under the combined action of waves and moving loads, the water inflow into multiple damaged compartments changes constantly. Coupled with the effect of free surface sloshing within the compartments, the mass distribution and additional hydrodynamic characteristics of the bridge sections exhibit strong nonlinear and unsteady features. The coupling effect between the internal and external flow fields of the entire floating bridge system and the bridge section structure is significant, resulting in a complex dynamic response. Existing technologies for predicting the dynamic response of such systems mainly face the following three technical challenges:

[0008] (1) Insufficient coupling of numerical analysis models: Existing time-domain methods based on multibody dynamics and potential flow theory usually simplify the pontoon bridge into a multi-rigid-body system, failing to effectively account for the coupling effect between the unsteady hull breach and water ingress process and the nonlinear motion of the connecting bridge sections. This method ignores the time-varying effects of the bridge section mass, center of gravity, moment of inertia, and additional hydrodynamic characteristics caused by water ingress, and also fails to consider the unsteadiness of the key motion parameter of the liquid tank sloshing frequency, resulting in distorted prediction of the system's dynamic response.

[0009] (2) There is a contradiction between computational efficiency, accuracy and analysis cost: Although high-precision computational fluid dynamics methods can simulate the dynamic response of a pontoon bridge damaged by waves and flooding, they consume a lot of computational resources and are extremely inefficient, making it difficult to meet the needs of rapid analysis and multi-condition evaluation in engineering practice. Although model testing can directly obtain dynamic response data of a pontoon bridge damaged by waves and flooding, it has shortcomings such as high testing costs, long testing cycles and difficulty in conducting multi-parameter influence studies.

[0010] (3) Dynamic analysis of a pontoon bridge without specific consideration of the time-varying effect of dammed water ingress: The existing technical solutions lack a unified theoretical framework and are difficult to deal with the dynamic coupling effect between nonlinear connecting bridge sections and unsteady dammed water ingress process under the combined action of complex waves and moving loads. Therefore, it is impossible to accurately predict the motion response and structural internal force peak of the dammed pontoon bridge, and it is also difficult to accurately assess its overall safety, stability and remaining load-bearing capacity in the dammed state.

[0011] In summary, existing methods have significant shortcomings in describing the time-varying water inflow and outflow process of damaged floating bridges and predicting the dynamic response of nonlinearly connected floating bridges with multiple compartments under wave action. There is still a lack of a method that can guarantee both computational efficiency and high accuracy for predicting the dynamic response of nonlinearly connected floating bridges with time-varying water inflow under the combined action of waves and moving loads. Summary of the Invention

[0012] The purpose of this invention is to provide a nonlinear connected floating bridge dynamic response prediction method that considers the time-varying effect of multi-compartment water ingress in waves. By establishing a liquid tank model in still water zone, a database of additional hydrodynamic coefficients and wave excitation load transfer functions, and a time-varying model of water volume in damaged compartments, the method achieves joint time-domain solution of water ingress load, additional hydrodynamic load, wave excitation load, and nonlinear connection load, thereby improving prediction accuracy and computational efficiency.

[0013] To achieve the objective of this invention, a method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effects of multi-compartment water ingress in waves is provided, comprising the following steps:

[0014] Step 1: Based on the parameters of the nonlinear connecting floating bridge, establish a nonlinear connector dynamic model and a nonlinear connecting floating bridge with liquid tanks in still water dynamic analysis model. Based on different combinations of the position, quantity and mass of the liquid tanks, determine the position coordinates and inclination angle of each bridge section when the floating bridge reaches equilibrium.

[0015] Step 2: Based on specific wave frequency and wave direction, considering the working conditions of liquid tanks with different locations, quantities, and masses, and using the water depth and the position coordinates and inclination angle of each bridge section when the floating bridge reaches equilibrium, establish a numerical model through potential flow theory, determine the additional hydrodynamic coefficients of each bridge section, as well as the amplitude and phase of wave excitation load per unit wave amplitude, and construct an additional hydrodynamic coefficient database and a wave excitation load transfer function database related to the location, quantity, mass, wave frequency, and wave direction of the liquid tanks.

[0016] Step 3: Establish a time-varying model of water volume in the damaged compartments during waves. The initial state for dynamic response analysis is that no water enters any of the damaged compartments. Based on the breach area of ​​each damaged compartment, the wave dynamic pressure at the breach, and the difference in liquid level between the inside and outside, the water ingress load is obtained. Based on the additional hydrodynamic coefficient database and the wave excitation load transfer function database, the additional hydrodynamic load and the wave excitation load are determined respectively.

[0017] Step 4: Substitute the nonlinear connector dynamic analysis model, inflow load, additional hydrodynamic load, and wave excitation load into the time-domain hydrodynamic analysis equation of the nonlinear connection floating bridge with time-varying water volume in multiple compartments under waves to obtain the dynamic response results of the floating bridge with time-varying water volume in the damaged compartments.

[0018] The significant advancement of this invention compared to existing technologies lies in:

[0019] (1) This invention incorporates the time-varying effect of multi-chamber water intake, nonlinear connection load, moving load, additional hydrodynamic and wave excitation load into a unified time-domain coupling analysis framework, which can more realistically reflect the dynamic characteristics of the damaged floating bridge in waves.

[0020] (2) By establishing an additional hydrodynamic coefficient database and a wave excitation load transfer function database associated with the location, quantity, mass, wave frequency and wave direction of the liquid tank, the present invention can be called or interpolated in real time in time domain analysis, which significantly improves the calculation efficiency.

[0021] (3) The present invention uses the modified Bernoulli equation to construct a time-varying model of water volume in the damaged compartment, which can reasonably reflect the influence of the breach area, wave dynamic pressure at the breach and the difference between the inner and outer liquid levels on the water ingress process, and improve the accuracy of water ingress load calculation.

[0022] (4) The present invention establishes time-domain hydrodynamic analysis equations based on the Kane method and solves them by combining the fourth-order Runge-Kutta method, which can simultaneously obtain the bridge section motion response and connector load, providing a basis for the safety assessment and structural design of floating bridges.

[0023] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0024] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0025] Figure 1 This is a flowchart of the overall process for analyzing the dynamic response of a continuously loaded floating bridge considering the time-varying effects of multi-section and multi-compartment damage and water ingress in waves, according to an embodiment of the present invention.

[0026] Figure 2 This is a flowchart of the dynamic response analysis method for a multi-section, multi-compartment floating bridge damaged by waves and flooding according to an embodiment of the present invention;

[0027] Figure 3 This is a top view schematic diagram of the floating bridge structure with multiple bridge sections and multiple compartments damaged and flooded in waves according to the present invention;

[0028] Figure 4 This is a side view schematic diagram of the wave-damaged, multi-section, multi-compartment floating bridge structure of the present invention.

[0029] Figure 5 This is a top view schematic diagram of the moving load on one bridge section of the multi-section, multi-compartment damaged and flooded floating bridge of the present invention;

[0030] Figure 6 This is a diagram showing the water ingress mass of a pontoon bridge section damaged in the middle, obtained by using the nonlinear connected pontoon bridge dynamic response prediction method of this invention, which considers the time-varying effect of multi-compartment water ingress in waves, when a moving load passes through a pontoon bridge under the action of regular waves of different frequencies.

[0031] Figure 7This is a comparison of the vertical displacement of the middle damaged bridge section of the floating bridge when a moving load passes under the action of regular waves, using the nonlinear connection floating bridge dynamic response prediction method that considers the time-varying effect of water ingress in the waves and the nonlinear connection floating bridge dynamic response prediction method that does not consider the time-varying effect of water ingress when a moving load passes under the action of regular waves.

[0032] Figure 8 This is a diagram showing the vertical shear force of a damaged section of a floating bridge under the action of regular waves of different frequencies. The method used in this invention is a nonlinear connection floating bridge dynamic response prediction method that considers the time-varying effect of water ingress in multiple compartments during waves.

[0033] Figure 9 This invention relates to an example of a moving load traveling on a floating bridge with hinges of varying rotational stiffness under the action of a regular wave. The method described in this invention is a nonlinear connection dynamic response prediction method for a continuously loaded floating bridge that considers the time-varying effect of water ingress in multiple compartments during waves. The diagram shows the bending moment load of the connector on the right side of the damaged bridge section in the middle of the floating bridge.

[0034] The attached diagram is labeled as follows: 1. Cabin; 2. Bridge section; 3. Nonlinear connector; 4. Hinged joint; 5. Pressure bearing seat; 6. Cable; 7. Anchor; 8. Moving load. Detailed Implementation

[0035] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] This invention provides a nonlinear connected floating bridge dynamic response prediction method considering the time-varying effects of multi-compartment water ingress in waves, combined with... Figure 1 and Figure 2 This includes the following steps:

[0037] Step 1: Based on the parameters of the nonlinear connecting floating bridge system, establish a nonlinear connector dynamic model and a nonlinear connecting floating bridge dynamic analysis model with liquid tanks in still water. For different combinations of liquid tank position, quantity and mass, determine the position coordinates and inclination angle of each bridge section when the system reaches equilibrium.

[0038] The floating bridge system parameters include: the number of bridge sections, parameters of each bridge section, the number of liquid tanks, the location of the liquid tanks, the mass of the liquid tanks, the parameters of the connectors between bridge sections, and the parameters of the mooring system; such as Figures 3-4As shown, a single bridge section 2 comprises several transversely and longitudinally arranged compartments 1. The floating bridge consists of several bridge sections 2, which are sequentially connected along the length direction to form the main structure of the floating bridge. The parameters of each bridge section 2 include the number and size of the compartments 1, the length, width, height, mass, moment of inertia, center of mass position, initial velocity, and initial angular velocity. The bridge sections are connected by nonlinear connectors 3. The connectors mainly include hinged joints 4 and pressure bearing seats 5. The mooring system of the floating bridge mainly includes anchors 7 for positioning and cables 6 for connecting the bridge sections 2 to the anchors 7.

[0039] First, based on the number, location, and mass of the liquid tanks, determine the contents. The total mass of the liquid tanks in the kth bridge section of the liquid tanks is: ;in, Let be the mass of the j-th liquid tank in the k-th bridge section; the change in the moment of inertia matrix of the bridge section caused by the j-th liquid tank in the k-th bridge section is:

[0040] ;

[0041] in, , and These are the x-coordinate, y-coordinate, and vertical coordinates of the center of mass of the j-th liquid tank in the k-th bridge section, located at the origin of the center of mass floating on the waterline of the intact bridge section, respectively.

[0042] The change in moment of inertia of the k-th bridge section caused by all liquid tanks is: ;

[0043] Then, a nonlinear connector 3 is established between the bridge sections using a constraint hinge. Before the constraint hinge closes, the relative rotational displacement stiffness between the bridge sections is zero, and after the constraint hinge closes, the rotational stiffness is... That is, the stiffness of the nonlinear connector 3 is:

[0044] ;

[0045] in, This represents the rotational displacement of the (k+1)th bridge segment relative to the kth bridge segment about the y-axis; This represents the closing angle of the k-th connector (restricting hinge);

[0046] The torque applied by the k-th connector (located between the k-th and (k+1)-th bridge sections) at its connection point to the k-th bridge section is:

[0047] ;

[0048] The force exerted on the k-th bridge section by the nonlinear connectors at both ends is: ;in, This represents the force exerted by the (k-1)th connector (located between the (k-1)th and kth bridge sections) at its connection point on the (k-1)th bridge section;

[0049] The torque exerted on the k-th bridge section by the nonlinear connectors at both ends is:

[0050] ;

[0051] in, This represents the force exerted by the (k-1)th connector (located between the (k-1)th and kth bridge sections) at its connection point on the (k-1)th bridge section; This represents the position vector from the centroid of the k-th bridge segment to its connection point with the (k+1)-th bridge segment; This represents the position vector from the centroid of the k-th bridge segment to its connection point with the (k-1)-th bridge segment.

[0052] Based on the geometric dimensions, mass, moment of inertia, and center of mass of each bridge section, and considering the combined effects of liquid tank load, still water recovery load, connector load, and mooring load on the bridge section, a nonlinear dynamic analysis model of a floating bridge with liquid tanks in still water is established.

[0053] ;

[0054] in, , , These are the target degree of freedom number, the summation degree of freedom number, and the hydrodynamic direction degree of freedom number, respectively. and The first one changes with time, respectively The degree of freedom and the first The generalized rate corresponding to each degree of freedom is the relative rotational rate and the translational rate between bridge sections; and The first one changes with time, respectively The bridge section is relative to the first The degree of freedom and the first The m-th component of a partial velocity array with a degree of freedom; and The first one changes with time, respectively The bridge section is relative to the first The degree of freedom and the first The m-th component of a deflection angular velocity array with a degree of freedom; For the first time to change The bridge section is relative to the first The r-th component of a deflection angular velocity array with a degree of freedom; For the first time to change The bridge section is relative to the first The nth component of a deflection angular velocity array with a degree of freedom; and The first one changes with time, respectively The bridge section is relative to the first The m-th component of the first-order derivative array of partial velocities and angular velocities with a degree of freedom; and The first The mass and moment of inertia matrix of the bridge section without liquid tanks. Line number Column elements; and They are respectively the first that does not change with time. In the matrix of the total mass of the liquid tanks in each bridge section and the resulting change in the moment of inertia of the bridge section, the first... Line number Column elements; and The first in still water The element in the m-th row and n-th column of the additional mass and additional inertia matrix of each bridge segment; Let the generalized rate correspond to the p-th degree of freedom that varies with time. The first derivative; and They represent the first The m-th component of the time-varying torque caused by the gravity acting on the liquid tank within each bridge section. and The first one changes with time, respectively The m-th component of the hydrostatic restoring force and moment of each bridge section; and The first one changes with time, respectively The m-th component of the mooring force and mooring moment acting on each bridge section; and The first one changes with time, respectively The m-th component of the force and torque caused by the connector of each bridge section; Let be the element in the r-th row, m-th column of the permutation matrix.

[0055] The dynamic equations of a nonlinear connected floating bridge with liquid tanks in still water are first-order ordinary differential equations concerning the generalized rate. A fourth-order Runge-Kutta method is used for time-domain numerical solution to determine the generalized rate at time t, which in turn allows determination of the position and inclination angle of each bridge segment at time t. As the time step progresses, the nonlinear connected floating bridge system with liquid tanks eventually tends towards a stable equilibrium state in still water.

[0056] Finally, based on the different locations, quantities, and mass conditions of the liquid tanks, the above equations are solved to obtain the position coordinates and inclination angles of each bridge section in the system under different stable equilibrium conditions.

[0057] Step 2: Based on the water depth, number of bridge sections, structural parameters, location, quantity, and mass of the liquid tanks, and the inclination angle and location of each bridge section determined in Step 1, establish the geometric model of the bridge sections and divide them into compartments and allocate the mass of the liquid tanks. After completing the wet surface mesh generation, sequentially set each bridge section in the system to operate at a wave frequency in each degree of freedom direction. Perform simple harmonic motion with unit velocity amplitude. For each unit motion, solve for the normalized velocity potential by combining the object surface boundary conditions, free surface boundary conditions, bottom boundary conditions, and far-field radiation conditions. Laplace's equation for (the spatial radiation potential generated by the motion with a unit velocity amplitude in the direction of the p-th degree of freedom) The normalized velocity potential corresponding to each degree of freedom is obtained, and then the wave frequency corresponding to each degree of freedom of each bridge section is determined. Generalized added mass coefficient and radiation damping coefficient ;in, This represents the normalized velocity potential corresponding to the l-th degree of freedom; Indicates the wet surface of each bridge section; This represents the normalized velocity potential corresponding to the p-th degree of freedom. Find the partial derivative along the wet surface normal.

[0058] For different frequencies The solution process after meshing is repeated for the working conditions of liquid tank location, quantity and mass to obtain a database of generalized additional mass coefficient and radiation damping coefficient.

[0059] Determine the wave frequency using the Haskind relation. , wave direction The wave excitation load transfer function for the l-th degree of freedom is:

[0060] ;

[0061] in, Represents the spatial incident potential per unit amplitude; Represents the spatial incident potential with respect to unit amplitude. Take the partial derivative along the wet surface normal.

[0062] For different frequencies , wave direction The solution process after meshing is repeated for the working conditions of liquid tank location, quantity, and mass, resulting in a wave excitation load transfer function database indexed by liquid tank location, quantity, mass, wave frequency, and wave direction.

[0063] Step 3: First, a time-varying model of water volume in a damaged compartment during waves is constructed based on the modified Bernoulli equation. This model is calculated by integrating the flow rate over time, based on the breach area, wave dynamic pressure at the breach, and the difference in liquid level between the inside and outside of the damaged compartment. Time of the first The water ingress mass of the j-th damaged compartment in the bridge section:

[0064] ;

[0065] in, This represents the flow coefficient related to the breach geometry, bridge joint motion, and compartment layout. Indicates the density of water; It is the acceleration due to gravity; The operator that determines the sign of the function value within the square brackets; and These represent the changes over time. The heights of the external and internal liquid levels in the j-th damaged compartment of a bridge section; Indicates the change over time. Wave dynamic pressure at the breach in the j-th compartment of the bridge section; Represents an area element; Indicates the area of ​​the breach; the first The external liquid level in the j-th damaged compartment of the bridge section is:

[0066] ;

[0067] in, , , They represent the first The horizontal, vertical, and longitudinal coordinates of the breach center of the j-th damaged compartment in the bridge section in the global coordinate system; Indicates the change over time. The instantaneous wave height at the horizontal coordinate of the breach in the j-th damaged compartment of a bridge segment. Considering the incident wave as an Airy wave at depth h, then the... The incident potential at the center of the breach in the j-th damaged compartment of a bridge section is:

[0068] ;

[0069] in, Indicates the amplitude of the incident wave; Indicates wave number; Indicates the first The phase at the breach in the j-th damaged compartment of the bridge section. The instantaneous wave height at the horizontal coordinate of the breach in the j-th damaged compartment of the bridge section is:

[0070] ;

[0071] No. The wave dynamic pressure at the breach in the j-th compartment of the bridge section is:

[0072] ;

[0073] Then, based on the time-varying model of the mass of water entering the damaged compartment during the waves described above, it was determined that... The quality of water entering the damaged water inlet bridge section of each compartment Based on the location, size, and movement status of the damaged compartments, the following was determined: The centroid coordinates of the water ingress mass in the cabin at any given time ( , , ).

[0074] Based on the aforementioned influent mass and its centroid coordinates, determine the forces and torques caused by the influent, as well as the change in the moment of inertia of the bridge section; the weight change caused by the influent to the bridge section is as follows: The resulting heeling moment and pitching moment are respectively and .

[0075] No. The change in the moment of inertia matrix of a single bridge segment caused by water ingress into the j-th damaged compartment can be calculated using the mass of the water ingress into the compartment. and its centroid coordinates ( , , )calculate:

[0076] ;

[0077] For those The first compartment to be flooded The change in moment of inertia of each bridge section due to water ingress. It is obtained from the superposition of the effects of each damaged compartment. ;

[0078] Under different liquid tank numbers, locations, and quantity conditions determined in step 2, the wave frequency... Corresponding additional hydrodynamic coefficient and Substituting into the Kramer-Kronig relation It can determine the generalized additional mass coefficient of each degree of freedom of each bridge section as the frequency approaches infinity under different liquid tank numbers, locations and quantities. Indicates the damaged bridge section in terms of frequency During motion, the generalized additional mass coefficient generated by the p-th degree of freedom motion in the l-th degree of freedom, 0- A certain circular frequency in For all frequencies.

[0079] Then, the radiation damping coefficient was determined under different conditions of the number, location, and quantity of liquid tanks. Integral method to determine the velocity time delay function under different conditions of number, location, and quantity of liquid tanks. .

[0080] Additional hydrodynamic loads include additional mass generalized forces. and radiation damping generalized force .

[0081] in, The additional mass matrix elements, considering the influence of the internal and external flow fields of the bridge section, are used when the wave frequency approaches infinity. express Elements of the velocity-time delay function matrix at any given moment; express The angular velocity or velocity component along the direction of the l-th degree of freedom at any given moment; The elements of the rearranged matrix representing the deflection velocity and deflection angular velocity arrays are defined as follows:

[0082] ;

[0083] This represents the rearranged matrix elements of the derivative array of partial velocity and partial angular velocity.

[0084] The amplitude and phase are determined based on the wave excitation load transfer function as follows:

[0085] ;

[0086] ;

[0087] in, This represents the amplitude of the wave excitation force of the m-th component in the k-th bridge segment; This represents the phase of the m-th component of the wave excitation force experienced by the k-th bridge segment relative to the origin of the global coordinate system. This represents the amplitude of the wave excitation torque of the m-th component in the k-th bridge section; This represents the phase of the m-th component of the wave excitation torque experienced by the k-th bridge section relative to the origin of the global coordinate system.

[0088] The wave excitation force experienced by the bridge segment at time t is:

[0089] ;

[0090] In the formula, This represents the amplitude at the center of the k-th bridge segment;

[0091] The wave excitation torque experienced by the bridge segment at time t is:

[0092] ;

[0093] like Figure 5 As shown, the vertical components of all moving loads 8 on the bridge section at time t are then calculated respectively. Torque components about the longitudinal axis and the torque component about the horizontal axis .

[0094] in, This represents the number of moving loads acting on the k-th bridge section; Let u be the mass of the moving load acting on the k-th bridge segment; and These represent the lateral and longitudinal eccentric displacements of the position of the u-th moving load relative to the center of gravity of the intact bridge section, respectively.

[0095] The specific calculation methods for still water recovery load and mooring force load can refer to existing methods, and will not be elaborated here. Considering the combined effects of time-varying inflow load, wave excitation load, additional hydrodynamic load, moving load, still water recovery load, mooring load, and nonlinear connector load on the floating bridge, the time-domain hydrodynamic analysis equations for a nonlinearly connected floating bridge with time-varying water volume in multiple compartments under wave conditions are established based on the Kane method:

[0096] ;

[0097] In the formula, and These represent the changes over time. The element in the m-th row and n-th column of the matrix representing the total mass of water entering the damaged section of each bridge segment and the resulting change in the moment of inertia of the bridge segment; and These represent the changes over time. The m-th component of the force and the resulting rotational torque caused by the mass of water entering the damaged section of the bridge; and These represent the effects of time on the first... The m-th component of the wave excitation force and moment of each bridge section; and These represent the effects of time on the first... The m-th component of the force and moment caused by the moving load of each bridge section.

[0098] The time-domain hydrodynamic analysis equations for a nonlinearly connected floating bridge with time-varying water volume in waves, established based on the Kane method, are first-order ordinary differential equations concerning the generalized velocity. Based on the initial state of the system, the generalized velocity at time t can be determined using the fourth-order Runge-Kutta method for time-domain numerical solution. This yields the position and inclination of each bridge section at time t, allowing for updates to the static recovery load, mooring load, nonlinear connector load, and moving load. Furthermore, the wave dynamic pressure at the breach and the internal and external liquid level heights at time t are used to calculate... The changes in the mass of water entering the compartment, the water ingress load, and the moment of inertia caused by the water ingress are calculated by calling the additional hydrodynamic coefficient database and the wave excitation load transfer function database. The additional hydrodynamic load and wave excitation load at time are then used to determine... Motion response of the system and connector load at all times.

[0099] like Figure 6 As shown in this embodiment, the nonlinear connected floating bridge dynamic response prediction method considering the time-varying effect of multi-compartment water ingress in waves calculates the water ingress mass time history curve of the damaged middle section of the floating bridge. After the floating bridge reaches a stable state of water ingress in still water, it is loaded with regular waves with frequencies of 1.0 rad / s, 1.1 rad / s, and 1.2 rad / s.

[0100] like Figure 7 As shown, the vertical displacement time history curves of the damaged middle section of the floating bridge under the combined action of regular waves and moving loads are compared between the method of this embodiment (a nonlinear connected floating bridge dynamic response prediction method considering the time-varying effect of multi-compartment water ingress in waves) and the method without considering the time-varying effect of water ingress. The calculation condition is that the floating bridge is loaded after reaching a stable state in still water with water ingress through the damaged compartments.

[0101] like Figure 8 As shown in this embodiment, the time history curve of the vertical shear force of the damaged section of the floating bridge is obtained by the nonlinear connected floating bridge dynamic response prediction method considering the time-varying effect of multi-compartment water ingress in waves. The floating bridge is loaded after reaching a stable state in still water with the compartment water ingress. The regular wave frequencies are taken as 1.0 rad / s, 1.1 rad / s, and 1.2 rad / s, respectively.

[0102] like Figure 9 As shown, the bending moment load time history curves of the right connector of the damaged middle section of the floating bridge are obtained by using the nonlinear connection loading method of the floating bridge considering the time-varying effect of multi-chamber water in the waves, under different limiting hinge rotational stiffness (5MN·rad / s, 10MN·rad / s, 15MN·rad / s) after the flooding of the damaged hull in still water reaches steady state.

[0103] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0104] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effects of multi-compartment water ingress in waves, characterized in that, Includes the following steps: Step 1: Based on the parameters of the nonlinear connecting floating bridge, establish a nonlinear connector dynamic model and a nonlinear connecting floating bridge with liquid tanks in still water dynamic analysis model. Based on different combinations of the position, quantity and mass of the liquid tanks, determine the position coordinates and inclination angle of each bridge section when the floating bridge reaches equilibrium. Step 2: Based on specific wave frequency and wave direction, considering the working conditions of liquid tanks with different locations, quantities, and masses, and using the water depth and the position coordinates and inclination angle of each bridge section when the floating bridge reaches equilibrium, establish a numerical model through potential flow theory, determine the additional hydrodynamic coefficients of each bridge section, as well as the amplitude and phase of wave excitation load per unit wave amplitude, and construct an additional hydrodynamic coefficient database and a wave excitation load transfer function database related to the location, quantity, mass, wave frequency, and wave direction of the liquid tanks. Step 3: Establish a time-varying model of water volume in the damaged compartments during waves. The initial state for dynamic response analysis is that no water enters any of the damaged compartments. Based on the breach area of ​​each damaged compartment, the wave dynamic pressure at the breach, and the difference in liquid level between the inside and outside, the water ingress load is obtained. Based on the additional hydrodynamic coefficient database and the wave excitation load transfer function database, the additional hydrodynamic load and the wave excitation load are determined respectively. Step 4: Substitute the nonlinear connector dynamic analysis model, inflow load, additional hydrodynamic load, and wave excitation load into the time-domain hydrodynamic analysis equation of the nonlinear connection floating bridge with time-varying water volume in multiple compartments under waves to obtain the dynamic response results of the floating bridge with time-varying water volume in the damaged compartments.

2. The method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effect of multi-compartment water ingress in waves, as described in claim 1, is characterized in that... Step 1 includes the following steps: Step 1-1: Determine the total mass of the liquid tanks within the bridge section and its change with respect to the moment of inertia of the bridge section based on the geometric dimensions, quantity, location, and mass of the liquid tanks. Steps 1-2: Based on the connector type and parameters between bridge sections, as well as the nonlinear constitutive relationship between the relative motion between bridge sections and the connector load, establish a nonlinear connector dynamic model, and determine the connector load by combining the motion state of the bridge sections. Steps 1-3: Based on the geometric dimensions, mass, moment of inertia, and center of mass position of each bridge section, combined with the total mass of the liquid tank inside the bridge section and its change on the moment of inertia of the bridge section, and considering the combined effects of the static water recovery load, connector load, and mooring load on the bridge section, establish a nonlinear connected floating bridge dynamic analysis model with liquid tank in static water. Steps 1-4: Using a nonlinear connected floating bridge dynamic analysis model with liquid tanks in still water, numerical calculations are carried out under liquid tank conditions of different positions, quantities, and masses to determine the position coordinates and inclination angles of each bridge section when the floating bridge reaches equilibrium under each working condition.

3. The method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effect of multi-compartment water ingress in waves, as described in claim 2, is characterized in that... Steps 1-2 are specifically as follows: Based on the connector type, parameters, and nonlinear constitutive relation between bridge segments, determine the force exerted by the k-th connector at its connection point on the k-th bridge segment between the k-th and (k+1)-th bridge segments. and torque The specific formula is as follows: ； in, The stiffness matrix is ​​related to the relative translational and rotational displacements between bridge sections; Let be the translational displacement of the (k+1)th bridge segment relative to the kth bridge segment; Let be the rotational displacement of the (k+1)th bridge segment relative to the kth bridge segment; The stiffness matrix is ​​related to the relative velocity and angular velocity between bridge sections; Let be the velocity of the (k+1)th bridge segment relative to the kth bridge segment; Let be the angular velocity of the (k+1)th bridge segment relative to the kth bridge segment; The k-th bridge section is subjected to the force of the nonlinear connectors at both ends, as shown in the following formula: ； in, The force applied to the (k-1)th bridge segment by the (k-1)th connector located between the (k-1)th and (k)th bridge segments at its connection point; The k-th bridge section is subjected to torque from the nonlinear connectors at both ends, as shown in the following formula: ； in, The torque applied to the (k-1)th bridge section by the (k-1)th connector located between the (k-1)th and (k)th bridge sections at its connection point; Let be the position vector pointing from the centroid of the k-th bridge segment to its connection point with the (k+1)-th bridge segment; Let be the position vector pointing from the centroid of the k-th bridge segment to its connection point with the (k-1)-th bridge segment.

4. The method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effect of multi-compartment water ingress in waves, as described in claim 3, is characterized in that... The nonlinear connected floating bridge dynamic analysis model with liquid tanks in still water, as described in steps 1-3, is shown in the following equation: ； in, , , These are the target degree of freedom number, the summation degree of freedom number, and the hydrodynamic direction degree of freedom number, respectively. and The first one changes with time, respectively The degree of freedom and the first The generalized rate corresponding to each degree of freedom is the relative rotational rate and the translational rate between bridge sections; and The first one changes with time, respectively The bridge section is relative to the first The degree of freedom and the first The m-th component of a partial velocity array with a degree of freedom; and The first and second are the changes over time. The bridge section is relative to the first The degree of freedom and the first The m-th component of a deflection angular velocity array with a degree of freedom; For the first time to change The bridge section is relative to the first The r-th component of a deflection angular velocity array with a degree of freedom; For the first time to change The bridge section is relative to the first The nth component of a deflection angular velocity array with a degree of freedom; and The first one changes with time, respectively The bridge section is relative to the first The m-th component of the first-order derivative array of partial velocities and angular velocities with a degree of freedom; and The first The mass and moment of inertia matrix of the bridge section without liquid tanks. Line number Column elements; and They are respectively the first that does not change with time. In the matrix of the total mass of the liquid tanks in each bridge section and the resulting change in the moment of inertia of the bridge section, the first... Line number Column elements; and The first in still water The element in the m-th row and n-th column of the additional mass and additional inertia matrix of each bridge segment; Let the generalized rate correspond to the p-th degree of freedom that varies with time. The first derivative; and They represent the first The m-th component of the time-varying torque caused by the gravity acting on the liquid tank within each bridge section. and The first one changes with time, respectively The m-th component of the hydrostatic restoring force and moment of each bridge section; and The first one changes with time, respectively The m-th component of the mooring force and mooring moment acting on each bridge section; and The first one changes with time, respectively The m-th component of the force and torque caused by the connector of each bridge section; Let be the element in the r-th row, m-th column of the permutation matrix.

5. A method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effect of multi-compartment water ingress in waves, as described in claim 4, is characterized in that... Step 2 specifically involves: Based on the water depth conditions and the positions and inclination angles of each bridge section determined in step 1, the radiation problem is solved for different wave frequencies using potential flow theory to determine the normalized velocity potential. The additional hydrodynamic coefficients of each bridge section at different wave frequencies are obtained by integration. Combining the known incident potential and Haskind relation, the wave excitation load transfer function is determined. The additional hydrodynamic coefficients include the generalized additional mass coefficient. and radiation damping coefficient By having one of its bridge sections operate at a given frequency in one degree of freedom. Performing simple harmonic motion with a unit velocity amplitude, the radiation velocity potential caused by this motion is solved. Then, by integrating the pressure over all wetted surfaces of the bridge sections, the radiation force generated by this motion on all 6N degrees of freedom is obtained. From this radiation force, the components related to motion acceleration and velocity are extracted to obtain the generalized added mass coefficient and radiation damping coefficient corresponding to this degree of freedom. Combining the generalized added mass coefficient and radiation damping coefficient corresponding to the 6N degrees of freedom, the wave frequency is obtained. Generalized additional mass coefficient and radiation damping coefficient ; The wave excitation load transfer function The specific formula is as follows: ； In the formula, Represents the spatial incident potential per unit amplitude; Represents the spatial incident potential with respect to unit amplitude. Find the partial derivative along the wet surface normal of the bridge section. Indicates frequency, Indicates wave direction, Represents the imaginary unit. This indicates the density of water. Indicates the first Radiation potential per unit velocity in one degree of freedom Represents the velocity potential Find the partial derivative along the wet surface normal of the bridge section. Represents an area element. This indicates the wetted surface area of ​​the bridge joint; By considering the different locations, quantities, masses, wave frequencies, and wave directions of the liquid tanks, the radiation velocity potential is solved based on potential flow theory. Combined with the aforementioned Haskind relation, an additional hydrodynamic coefficient database and a wave excitation load transfer function database with the above parameters as multiple indices are obtained.

6. The method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effect of multi-compartment water ingress in waves, as described in claim 5, is characterized in that... Step 3 specifically includes the following steps: Step 3-1: Construct a time-varying model of water volume in a damaged compartment during a wave based on the modified Bernoulli equation. This model is used to determine the water ingress mass of the damaged compartment based on the breach area, wave dynamic pressure at the breach, and the difference in liquid level between the inside and outside of the damaged compartment. Step 3-2: Based on the water ingress mass of the damaged compartment, determine the water ingress mass of the damaged bridge section, and in conjunction with the location of the damaged compartment, the size of the compartment, and the motion state of the bridge section, determine the coordinates of the center of mass of the water ingress mass in the compartment; based on the water ingress mass of the compartment and the coordinates of its center of mass, determine the time-varying load of water ingress and the change in the moment of inertia of the bridge section, wherein the time-varying load of water ingress includes the force and torque caused by water ingress; Step 3-3: Substitute the additional hydrodynamic coefficients into the Kramers-Kronig relation to determine the generalized additional mass coefficients of each degree of freedom of each bridge section as the frequency approaches infinity; integrate the radiation damping coefficients at different frequencies to determine the velocity time delay function at time t, and thus obtain the additional hydrodynamic load; obtain the wave excitation load based on the actual wave amplitude and the wave excitation load transfer function containing wave amplitude and phase information; determine the force and moment acting on the bridge section caused by the moving load based on the mass and eccentricity of the moving load.

7. A method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effect of multi-compartment water ingress in waves, as described in claim 6, is characterized in that... In step 3-1, a time-varying model of water volume in a damaged compartment during waves is constructed based on the modified Bernoulli equation; the model is then calculated by integrating the flow rate over time based on the breach area, wave dynamic pressure at the breach, and the difference in liquid level between the inside and outside of the damaged compartment. Time of the first The water ingress quality of the j-th damaged compartment in the bridge section The specific formula is as follows: ； in, The flow coefficient is related to the breach geometry, bridge joint motion, and compartment layout. The density of water; It is the acceleration due to gravity; An operator for determining the sign of the function value within parentheses; and The first one changes with time, respectively The heights of the external and internal liquid levels in the j-th damaged compartment of a bridge section; The wave-like pressure at the breach varies over time; For time infinitesimal elements; This represents the area of ​​the breach. No. The external liquid level height of the j-th damaged compartment in a bridge section is given by the following formula: ； in, , , They represent the first The horizontal, vertical, and longitudinal coordinates of the breach center of the j-th damaged compartment in the bridge section in the global coordinate system; Indicates the change over time. The instantaneous wave height at the horizontal coordinate of the breach in the j-th damaged compartment of the bridge section.

8. A method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effects of multi-compartment water ingress in waves, as described in claim 7, is characterized in that... The additional hydrodynamic load in step 3-3 includes the additional mass generalized force. and radiation damping generalized force ; in, The additional mass matrix elements are those that consider the influence of the flow fields inside and outside the bridge section when the wave frequency approaches infinity. for Elements of the velocity-time delay function matrix at any given moment; for The angular velocity or velocity component along the direction of the l-th degree of freedom at any given moment; Rearrange the matrix elements for the deflection velocity and deflection angular velocity arrays: ; This represents the rearranged matrix elements of the array of derivatives of partial velocity and partial angular velocity; The wave excitation load on the bridge segment at time t is obtained based on the actual wave amplitude and the wave excitation load transfer function containing wave amplitude and phase information: Wave excitation force on the bridge segment at time t: ； in, This represents the amplitude at the center of the k-th bridge segment; This represents the amplitude of the wave excitation force of the m-th component in the k-th bridge segment; This represents the phase of the m-th component of the wave excitation force experienced by the k-th bridge segment relative to the origin of the global coordinate system. Wave excitation torque on bridge segment at time t : ； in, This represents the amplitude of the wave excitation torque of the m-th component in the k-th bridge section; This represents the phase of the m-th component of the wave excitation torque experienced by the k-th bridge section relative to the origin of the global coordinate system. Next, the vertical components of all moving loads acting on the bridge section at time t are calculated. Torque components about the longitudinal axis and the torque component about the horizontal axis ; in, This represents the number of moving loads acting on the k-th bridge section; Let u be the mass of the moving load acting on the k-th bridge segment; and These represent the lateral and longitudinal eccentric displacements of the position of the u-th moving load relative to the center of gravity of the intact bridge section, respectively.

9. A method for predicting the dynamic response of a nonlinearly connected, continuously loaded floating bridge considering the time-varying effect of multi-compartment water ingress in waves, as described in claim 8, is characterized in that... Step 4 specifically involves: considering the combined effects of time-varying inflow loads, wave-induced loads, additional hydrodynamic loads, moving loads, still-water recovery loads, mooring loads, and connector loads on the floating bridge, and establishing time-domain hydrodynamic analysis equations for a nonlinearly connected floating bridge with time-varying water volume in waves based on the Kane method: ； In the formula, and These represent the changes over time. The element in the m-th row and n-th column of the matrix representing the total mass of water entering the damaged section of each bridge segment and the resulting change in the moment of inertia of the bridge segment; and These represent the changes over time. The m-th component of the gravity and the resulting rotational torque corresponding to the mass of water entering the damaged section of the bridge; and These represent the effects of time on the first... The m-th component of the wave excitation force and moment of each bridge section; and These represent the effects of time on the first... The m-th component of the force and moment caused by the moving load of each bridge section; The generalized velocity at time t is determined by using the fourth-order Runge-Kutta method in the time domain. This allows us to determine the position and inclination of each bridge segment, as well as the shear force and bending moment at the connector at time t. During the dynamic analysis, the corresponding additional hydrodynamic coefficients and wave excitation load transfer functions are retrieved in real time from the additional hydrodynamic coefficient database and the wave excitation load transfer function database, or obtained through multidimensional interpolation, based on the current state parameters. The hydrostatic restoring force and moment, as well as the mooring force and moment, are determined based on the inclination and position of the bridge segments.

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