A method and system for solving response of ice-structure based on non-linear energy sink

Abstract

The present application relates to the technical field of ice-induced vibration control and dynamic response of marine structures, and particularly relates to an ice-induced structure response solving method and system based on a nonlinear energy sink. The method establishes a multi-order modal dynamic equation of the structure and introduces a nonlinear energy sink degree of freedom to form an extended dynamic equation. In each time step, the Newmark-beta method is used to predict the response, and the ice crushing strength is directly mapped to the contact strength without the need for ice spring deformation and crushing correction based on the segmented ice force model of the stress rate-dependent ice crushing strength in the Newton iteration to calculate the dynamic ice force. Further, the ice force velocity feedback derivative is used to form an extended equivalent stiffness term, which is assembled with the nonlinear action term of the nonlinear energy sink to form a total equivalent stiffness matrix for implicit iteration solving. After convergence, the ice force negative damping excitation state and the net negative damping state of the controlled system are identified. The present application realizes the strong coupling and stable solving of the ice force velocity feedback and the nonlinearity of the nonlinear energy sink.

Description

Technical Field

[0001] This invention relates to the field of ice-induced vibration control and dynamic response technology for marine structures, specifically to a method and system for solving the response of ice-induced structures based on a nonlinear energy trap. Background Technology

[0002] Marine structures in ice-covered areas are prone to ice-induced vibrations under the influence of sea ice. For flexible marine structures, when ice interacts with the structure, the ice force is not always an external load independent of the structural response, but is significantly affected by the relative velocity between the ice and the structure. In particular, in the ice crushing strength model related to stress rate, the ice crushing strength changes with the relative velocity. When the ice strength curve is in the descending segment, the derivative of the ice force with respect to the relative velocity between the ice and the structure may generate a negative damping effect, causing the structural response to gradually increase and enter a frequency-locked steady-state vibration state. This ice-induced negative damping frequency-locked vibration poses a serious threat to the safety and fatigue life of marine structures.

[0003] Existing methods for simulating ice-induced vibrations use ice springs or Matlock-type contact elements to describe ice-structure interactions. These methods typically require calculating ice spring deformation and determining whether breakage has occurred at the current contact point by comparing the ice spring stress with the ice crushing strength related to the stress rate. If breakage is detected, the ice spring deformation needs to be reduced according to a preset breakage length, and correction calculations are performed. While these methods can describe local ice breakage processes, they involve numerous model variables. Furthermore, when strongly coupled with implicit iterations using additional nonlinear devices such as nonlinear energy traps, the frequent switching of contact states and the breakage correction process significantly increase nonlinear complexity, impacting computational efficiency and convergence stability.

[0004] Nonlinear energy traps are passive energy absorption devices with nonlinear stiffness (typically cubic stiffness) and damping energy dissipation capabilities. They possess advantages such as wide frequency response and strong parameter robustness, and have attracted widespread attention in the field of structural vibration control. However, in ice-induced negative damping frequency-locked vibration, the role of the nonlinear energy trap is not simply a linear addition of damping. Its cubic stiffness nonlinearity couples with the ice force velocity feedback nonlinearity, jointly affecting the structural dynamic response. If only the ice force and the nonlinear energy trap force are explicitly added to the dynamic equation as external forces, or if the ice force and control force are only updated outside the time step, the ice force negative damping feedback effect and the nonlinear energy trap nonlinear energy absorption effect cannot be solved in a coordinated manner in the same iterative equilibrium equation, which may lead to numerical instability or slow convergence.

[0005] Furthermore, existing negative damping criteria are mostly applied to ice-structure systems without nonlinear energy traps, primarily used to determine whether the velocity feedback term overcomes the structure's own damping and induces self-excited vibration. When a nonlinear energy trap is added to the system, in addition to determining whether the ice force has a negative damping excitation effect, it is also necessary to determine whether the ice force-structure-nonlinear energy trap controlled system after adding the nonlinear energy trap is still in a net negative damping state, in order to quantitatively assess the degree to which the nonlinear energy trap cancels out the negative damping effect of the ice force. However, there is currently a lack of methods and systems that can simultaneously achieve the above functions within a unified framework. Summary of the Invention

[0006] The purpose of this invention is to propose a method and system for solving the ice-induced structural response based on a nonlinear energy trap, so as to realize the synchronous identification of the ice-force negative damping excitation state and the net negative damping state of the controlled system, thereby improving the stability and convergence of the calculation of the ice-induced negative damping frequency-locked vibration response.

[0007] According to a first aspect of the present disclosure, a method for solving the response of an ice-induced structure based on a nonlinear energy trap is provided, comprising the following steps: Establish the multi-mode dynamic equations of the structure, determine the location of ice force action and the installation location of the nonlinear energy trap, and extract the corresponding mode shape vectors respectively; By introducing nonlinear energy trap degrees of freedom into the structural multimodal dynamic equations, an extended dynamic equations containing structural modal degrees of freedom and nonlinear energy trap degrees of freedom are formed. Entering the time step iteration, the Newmark-β method is used to construct the predicted displacement and predicted velocity in each time step. During the Newton iteration, the dynamic ice force is calculated using a piecewise ice force model based on stress rate-related ice crushing intensity, according to the current ice-structure relative velocity. The piecewise ice force model calculates the stress rate parameters and current ice crushing intensity of each segment according to the current ice-structure relative velocity, and maps the current ice crushing intensity to the current contact intensity to calculate the normal ice force, friction force and horizontal resultant force of each segment. The derivative of the dynamic ice force with respect to the relative velocity is obtained from the ice-structure relative velocity under the current iteration state, and the ice force velocity feedback extended equivalent stiffness term is formed from the obtained derivative. At the same time, the nonlinear action term of the nonlinear energy trap is obtained from the response of the structure at the nonlinear energy trap installation position and the response of the nonlinear energy trap mass block. The basic equivalent stiffness, the velocity feedback extended equivalent stiffness term, and the nonlinear energy trap nonlinear action term are assembled into a total equivalent stiffness matrix. The total equivalent stiffness matrix is ​​used to solve for the displacement correction in the current Newton iteration step, and the displacement, velocity, and acceleration of the structure and the nonlinear energy trap are updated until the convergence condition is met, thus obtaining the coupled dynamic response after convergence in the current time step. Based on the derivative of the converged dynamic ice force with respect to the relative velocity of ice and structure, identify and record the ice force negative damping excitation state at the current time step and the net negative damping state of the controlled system after adding the nonlinear energy trap. Repeat the above time step iterations until the preset total calculation time is reached, and output the structural response time history, dynamic icing force time history, nonlinear energy trap response time history, and negative damping identification results.

[0008] In one embodiment, the method for assembling the total equivalent stiffness matrix includes: Construct the Newmark basic equivalent stiffness matrix:

[0009] in, , , These are the extended mass matrix, extended damping matrix, and extended stiffness matrix, which contain structural modal degrees of freedom and nonlinear energy trap degrees of freedom, respectively. and For the integration parameters of the Newmark-β method, For time step; Based on the ice-structure relative velocity in the current Newton iteration step The derivative of the dynamic ice force with respect to the relative velocity of the ice and structure is obtained using the central difference method:

[0010] in, To preset the relative velocity disturbance, For dynamic ice force; the derivative is... Converted to the extended equivalent stiffness term of ice force velocity feedback in extended degree-of-freedom space:

[0011] in, This is the mode shape vector of the ice force at the location where the ice force acts; Construct the relative response vector of the nonlinear energy trap:

[0012] in, This is the mode shape vector at the mounting point corresponding to the nonlinear energy trap installation location; According to the extended displacement vector and extended velocity vector The relative displacement and relative velocity of the nonlinear energy trap are obtained:

[0013]

[0014] The velocity feedback extended equivalent stiffness term and the nonlinear energy trap nonlinear action term are combined to construct the ice force-nonlinear energy trap additional equivalent stiffness matrix:

[0015] in, The stiffness coefficient of the nonlinear energy trap. The damping coefficient of the nonlinear energy trap; The Newmark basic equivalent stiffness matrix and the ice force-nonlinear energy trap additional equivalent stiffness matrix are assembled together to form the total equivalent stiffness matrix: .

[0016] In one embodiment, the segmented ice force model divides the ice-facing contact area of ​​the structure into multiple computational blocks along the circumferential direction. Each computational block is based on the current ice-structure relative velocity. Calculate its radial relative velocity:

[0017] in, Let be the central angle of the j-th computational block, and be the ice crushing intensity of the j-th computational block. Determined according to the following segmentation method:

[0018]

[0019] Calculated based on the current ice crushing intensity. Contact stress of each calculation block:

[0020] And the normal ice force is obtained based on the area of ​​the calculated block:

[0021] The frictional force is obtained from the normal ice force:

[0022] No. The horizontal component of the force along the direction of ice velocity in each calculation block:

[0023] in, The diameter of the structure. Because the ice is thick, Let be the ice-structure friction coefficient; sum the horizontal components of the forces across all calculated blocks, and obtain the total dynamic ice force based on structural symmetry:

[0024] in, To calculate the number of blocks; In one embodiment, the method for identifying negative damping includes: According to ice speed Calculate the structural modal velocities at the locations where ice forces interact, and the relative velocities between the ice and the structure. ,in, The structural modal velocity vector, This represents the ice force mode shape vector corresponding to the location where the ice force acts; the dynamic ice force is expressed as a function of the relative velocity between the ice and the structure. And calculate the derivative of the dynamic ice force with respect to the relative velocity of the ice and structure near the convergence state at the current time step. ; Construct the ice force equivalent damping matrix based on the derivative. The equivalent damping matrix is ​​obtained by superimposing the ice force equivalent damping matrix with the structural damping matrix. When the equivalent damping matrix has negative damping characteristics, or the target mode satisfies When it is determined that the current time step exists in the state of ice force negative damping excitation, where For the first Step structure modal damping, The mode shape vector corresponding to the position where the ice force acts is at the th position. Components in the first mode; In an extended degree-of-freedom space containing the nonlinear energy trap degree of freedom, construct the nonlinear energy trap damping matrix. Ice force velocity feedback extended damping matrix and the structural extended damping matrix The total equivalent damping matrix of the ice force-structure-nonlinear energy trap controlled system is obtained as follows: When the total equivalent damping matrix of the controlled system has negative damping characteristics, or has an extended velocity vector Make At that time, it was determined that the system after adding the nonlinear energy trap was still in a state of net negative damping.

[0025] In one embodiment, when the relative velocity between the ice and the structure is in a preset near-zero velocity range, an ice force smoothing activation function is introduced. The original ice force obtained according to the piecewise ice force model is multiplied by the ice force smoothing activation function, so that the ice force transitions continuously from zero to the original ice force during the initial contact stage. The ice force smoothing activation function is:

[0026]

[0027] in, The relative velocity between the ice and the structure. The preset smoothing speed threshold.

[0028] In one embodiment, when establishing the multi-mode dynamic equations of the structure, the first few modes of the structure are selected for calculation. The structural modal mass matrix, structural modal damping matrix, and structural modal stiffness matrix are established based on the natural frequencies and mode shape data of the structure. The ice force mode shape vector corresponding to the ice force action position is extracted from the structural mode shape data based on the ice force action height. The installation point mode shape vector corresponding to the nonlinear energy trap installation position is extracted based on the nonlinear energy trap installation height.

[0029] In one embodiment, the output negative damping identification result includes the ice force negative damping excitation state time history and the controlled system net negative damping state time history; if the ice force negative damping excitation state exists but the controlled system net negative damping state does not exist, it is determined that the nonlinear energy trap has canceled the ice force negative damping effect in the current time step; the output structural response time history includes the structural displacement time history, the structural velocity time history and the structural acceleration time history, and the output nonlinear energy trap response time history includes the nonlinear energy trap displacement time history and the nonlinear energy trap relative travel time history.

[0030] According to a second aspect of the present disclosure, a system for solving the ice-induced structural response based on a nonlinear energy trap is provided, comprising: The structural modal modeling and mode shape extraction module establishes the multi-mode dynamic equations of the structure, determines the location of ice force action and the installation location of the nonlinear energy trap, and extracts the corresponding mode shape vectors respectively. An extended dynamic equation construction module introduces nonlinear energy trap degrees of freedom into the structural multimodal dynamic equations, forming extended dynamic equations that include structural modal degrees of freedom and nonlinear energy trap degrees of freedom. The time-step prediction and ice force calculation module enters the time-step iteration. Within each time step, the Newmark-β method is used to construct the predicted displacement and predicted velocity. During the Newton iteration, based on the current ice-structure relative velocity, a piecewise ice force model based on stress rate-related ice crushing intensity is used to calculate the dynamic ice force. The piecewise ice force model calculates the stress rate parameters and current ice crushing intensity of each segment based on the current ice-structure relative velocity, and maps the current ice crushing intensity to the current contact intensity to calculate the normal ice force, friction force, and horizontal resultant force of each segment. The velocity feedback and nonlinear action term calculation module obtains the derivative of the dynamic ice force with respect to the relative velocity based on the ice-structure relative velocity in the current iteration state, and forms the ice force velocity feedback extended equivalent stiffness term from the obtained derivative. At the same time, it obtains the nonlinear action term of the nonlinear energy trap based on the response of the structure at the nonlinear energy trap installation position and the response of the nonlinear energy trap mass block. The total equivalent stiffness assembly and Newton iteration solution module assembles the basic equivalent stiffness, the velocity feedback extended equivalent stiffness term, and the nonlinear energy trap nonlinear action term into a total equivalent stiffness matrix. The total equivalent stiffness matrix is ​​used to solve for the displacement correction in the current Newton iteration step, and the displacement, velocity, and acceleration of the structure and the nonlinear energy trap are updated until the convergence condition is met, thus obtaining the coupled dynamic response after convergence in the current time step. The negative damping state identification module identifies and records the ice force negative damping excitation state at the current time step and the net negative damping state of the controlled system after adding the nonlinear energy trap, based on the derivative of the converged dynamic ice force with respect to the relative velocity of ice and structure. The iterative loop and result output module repeats the above time step iterations until the preset total calculation time is reached, and outputs the structural response time history, dynamic icing force time history, nonlinear energy trap response time history, and negative damping identification results.

[0031] According to a third aspect of the present disclosure, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and running on the memory, wherein the processor executes the program to implement the aforementioned method for solving the ice-induced structural response based on a nonlinear energy trap.

[0032] According to a fourth aspect of the present disclosure, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the aforementioned method for solving the ice-induced structural response based on a nonlinear energy trap.

[0033] The advantages of the above technical solutions adopted in this invention compared with the prior art are as follows: First, this invention adopts a piecewise ice force model based on stress-rate-dependent ice crushing strength, which directly maps the stress-rate-dependent ice crushing strength to the current contact strength for ice force calculation. This avoids the additional nonlinear state variables brought about by the ice spring deformation degrees of freedom, breakage criterion switching, and breakage length correction in the traditional ice spring model, significantly simplifying the ice force calculation process. It also makes the calculation and assembly of the ice force velocity feedback derivative easier to implement in Newton iteration, reducing the numerical instability caused by abrupt changes in contact state.

[0034] Second, this invention constructs the ice force-nonlinear energy trap additional equivalent stiffness matrix by combining the ice force velocity feedback extended equivalent stiffness term and the nonlinear energy trap nonlinear action term, and assembles it together with the Newmark basic equivalent stiffness matrix to form the total equivalent stiffness matrix. This allows the ice force velocity feedback effect and the nonlinear energy trap nonlinear energy absorption effect to be solved in the same implicit iteration process, avoiding the coordination problem caused by explicitly treating ice force and control force as external forces, and effectively improving the computational convergence and stability under strong coupling conditions.

[0035] Third, this invention constructs an equivalent damping matrix of ice force based on the derivative of dynamic ice force with respect to the relative velocity of ice and structure. This matrix can identify and record the excitation state of negative damping ice force during time-domain calculations, providing a direct calculation basis for determining the initiation conditions and response growth mechanism of ice-induced frequency-locked vibrations.

[0036] Fourth, this invention further incorporates the nonlinear energy trap damping matrix into the total equivalent damping matrix in the extended degree-of-freedom space, which can quantitatively determine whether the ice force-structure-nonlinear energy trap controlled system is still in a net negative damping state after the addition of the nonlinear energy trap, thereby accurately reflecting the actual cancellation effect of the nonlinear energy trap on the ice force negative damping excitation, and providing a clear criterion for the effectiveness evaluation of the vibration reduction device.

[0037] Fifth, this invention can introduce a near-zero relative velocity ice force smoothing activation function, so that the ice force transitions continuously from zero to the original ice force in the initial contact stage, effectively reducing the ice force jump caused by hard switching between contact and separation, and further improving the numerical stability of nonlinear iterative solutions. Attached Figure Description

[0038] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0039] Figure 1 This is a schematic diagram of the ice-induced structural response solution method based on a nonlinear energy trap according to the present invention. Figure 2 This is a flowchart of the coupled iterative solution process after entering the time step in this invention; Figure 3 This is a flowchart illustrating the identification process between the excitation state of ice-force negative damping and the net negative damping state of the controlled system in this invention. Figure 4 This is a time history diagram of the displacement response of the ice-cold structure in an embodiment of the present invention. Detailed Implementation

[0040] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0041] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0042] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0043] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and systems according to various embodiments of this disclosure. It should be noted that each block in a flowchart or block diagram may represent a module, segment, or portion of code, which may include one or more executable instructions for implementing the logical functions specified in the various embodiments. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutively represented blocks may actually be executed substantially in parallel, or they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, may be implemented using a dedicated hardware-based system that performs the specified functions or operations, or using a combination of dedicated hardware and computer instructions.

[0044] Example 1: This embodiment takes a 10MW monopile offshore wind turbine in an ice-covered area as an example. The structure is represented by modal coordinates, and the nonlinear energy sink is installed at a preset height of the structure. The ice force acts near the sea surface.

[0045] A method for solving the response of ice-induced structures based on nonlinear energy traps, such as... Figure 1 As shown, it includes the following steps: S1. Establish the multi-mode dynamic equations of the structure, determine the location of ice force action and the installation location of the nonlinear energy trap, and extract the corresponding mode shape vectors respectively; In this embodiment, the structural dynamic parameters such as natural frequencies, mode shapes, modal masses, and damping ratios of the structure to be analyzed are first obtained. Several first-order modes of the structure are selected for subsequent calculations, thereby establishing the structural modal mass matrix, structural modal damping matrix, and structural modal stiffness matrix. Then, based on the height of the ice force application, the mode shape vector corresponding to the location of the ice force application is extracted from the structural mode shape data; simultaneously, based on the installation height of the nonlinear energy trap, the mode shape vector corresponding to the installation location of the nonlinear energy trap is extracted.

[0046] S2. Introduce nonlinear energy trap degrees of freedom into the multi-mode dynamic equations of the structure to form extended dynamic equations that include structural modal degrees of freedom and nonlinear energy trap degrees of freedom; In this embodiment, the nonlinear energy trap mass block is introduced as an additional degree of freedom into the structural multimodal dynamic equations, forming an extended dynamic equation that includes structural modal degrees of freedom and nonlinear energy trap degrees of freedom. In this extended dynamic equation, the structural modal mass matrix, structural modal damping matrix, and structural modal stiffness matrix constitute the basic dynamic system; the damping effect and nonlinear stiffness effect of the nonlinear energy trap are not pre-assembled into the system matrix as fixed linear matrices, but are updated and assembled in real time during the iteration process of each time step based on the current displacement and velocity response of the structure at the installation position of the nonlinear energy trap.

[0047] S3. Enter the time step iteration. In each time step, the Newmark-β method is used to construct the predicted displacement and predicted velocity. During the Newton iteration, based on the current ice-structure relative velocity, a piecewise ice force model based on stress rate-related ice crushing intensity is used to calculate the dynamic ice force. The piecewise ice force model calculates the stress rate parameters and current ice crushing intensity of each segment based on the current ice-structure relative velocity, and maps the current ice crushing intensity to the current contact intensity to calculate the normal ice force, friction force and horizontal resultant force of each segment. like Figure 2 As shown, the calculation conditions and integration parameters are set as follows: ice velocity is determined according to the target sea state, ice thickness is 0.2m, structure diameter is 9.5m, ice-structure friction coefficient is 0.2, ice strength adjustment coefficient is 2 / 3, time step is 0.005 s, total calculation time is 500s, and Newmark-β integration parameters and Newton iteration convergence tolerance are set.

[0048] At the start of the calculation, zero initial conditions are applied to the displacements of each mode of the structure and the displacements of the nonlinear energy trap mass block. Zero initial conditions are also applied to the velocities of each mode of the structure and the velocities of the nonlinear energy trap mass block. At the same time, the initial stress rate in the ice force model is set to zero. Based on this, the initial acceleration is calculated from the extended dynamic equations, and then the iterative calculation of the first time step begins.

[0049] At the beginning of each time step, the displacement, velocity, and acceleration of the current time step are predicted using the Newmark-β method after convergence of the displacement, velocity, and acceleration of the previous time step, and the predicted values ​​are used as the initial state vector for Newton iteration.

[0050] S4. Based on the ice-structure relative velocity in the current iteration state, obtain the derivative of the dynamic ice force with respect to the relative velocity, and form the ice force velocity feedback extended equivalent stiffness term from the obtained derivative. At the same time, based on the structure's response at the nonlinear energy trap installation location and the response of the nonlinear energy trap mass block, obtain the nonlinear action term of the nonlinear energy trap. In the current Newton iteration step, based on the structural modal velocities and the mode shape vector at the location of ice force application, the structural velocity at the location of ice force application is obtained, and the ice-structure relative velocity is also obtained:

[0051] in, For ice speed, The structural modal velocity vector, This is the mode shape vector of the ice force at the location where the ice force is applied.

[0052] A piecewise ice force model based on stress-rate-dependent ice crushing strength is used to calculate the current dynamic ice force. Specifically, the contact area of ​​the structure on the ice-facing side is divided into multiple calculation blocks along the circumference. For each calculation block, the radial relative velocity is determined based on the current ice-structure relative velocity, and then its stress-rate parameters and current ice crushing strength are calculated. Subsequently, the ice crushing strength is mapped to the current contact strength, and the normal ice force, frictional force, and horizontal component along the ice velocity direction are calculated for each calculation block. Finally, the horizontal components of each calculation block are summed to form the current total dynamic ice force. This process does not require the introduction of ice spring deformation degrees of freedom and breakage length correction. The ice crushing strength can be directly updated and integrated based on the current relative velocity at each step, which helps maintain the consistency of Newton iterations.

[0053] S5. Assemble the basic equivalent stiffness, the velocity feedback extended equivalent stiffness term, and the nonlinear energy trap nonlinear action term into a total equivalent stiffness matrix. Use the total equivalent stiffness matrix to solve for the displacement correction in the current Newton iteration step, and update the displacement, velocity, and acceleration of the structure and the nonlinear energy trap until the convergence condition is met, and obtain the coupled dynamic response after convergence in the current time step. In this embodiment, to account for the influence of ice force changes with the relative velocity of the ice-structure on the iterative solution, the derivative of the dynamic ice force with respect to the relative velocity of the ice-structure is calculated in the current Newton iteration step. This derivative is obtained using the central difference method, that is, the dynamic ice force values ​​are calculated when the relative velocity of the ice-structure increases and decreases by a preset disturbance amount, and then the derivative is obtained through difference. Based on the obtained derivative, an ice force velocity feedback extended equivalent stiffness term is constructed, so that the velocity feedback effect of the ice force is included in the total equivalent stiffness matrix of the current Newton iteration. Simultaneously, based on the current response of the structure at the nonlinear energy trap installation location and the current response of the nonlinear energy trap mass block, the relative displacement and relative velocity of the nonlinear energy trap are calculated, thereby determining its nonlinear stiffness contribution and damping contribution.

[0054] The overall equivalent stiffness matrix is ​​obtained as follows: First, construct the Newmark basic equivalent stiffness matrix; then, combine the ice force velocity feedback extended equivalent stiffness term with the nonlinear energy trap nonlinear action term to form the ice force-nonlinear energy trap additional equivalent stiffness matrix; finally, assemble the two together to form the overall equivalent stiffness matrix.

[0055]

[0056]

[0057]

[0058]

[0059] in, , , These are the extended mass matrix, extended damping matrix, and extended stiffness matrix, which contain structural modal degrees of freedom and nonlinear energy trap degrees of freedom, respectively. and For the integration parameters of the Newmark-β method, For time step, Let be the derivative of the dynamic ice force with respect to the relative velocity of the ice and the structure. This is the mode shape vector corresponding to the location where the ice force acts. The nonlinear energy trap cubic stiffness coefficient is... The damping coefficient of the nonlinear energy trap is... This represents the mode shape vector at the mounting point corresponding to the nonlinear energy trap installation location. For the Newmark basic equivalent stiffness matrix, It is the additional equivalent stiffness matrix formed by the ice force velocity feedback term and the nonlinear energy trap nonlinear action term.

[0060] Subsequently, the displacement correction is calculated based on the current dynamic equilibrium residual, and the displacement, velocity, and acceleration of the structure and the nonlinear energy trap are updated simultaneously.

[0061] Preferably, the convergence condition is determined by combining the displacement correction norm and the dynamic equilibrium residual norm: If the current iteration step does not meet the convergence condition, return to the beginning of the current time step, recalculate the ice-structure relative velocity, piecewise ice force, ice force-velocity feedback derivative, nonlinear energy trap relative response, total equivalent stiffness matrix and displacement correction based on the updated iteration state, and continue to the next round of Newton iteration.

[0062] If the convergence condition is met, the iteration at the current time step ends, and the ice-structure-nonlinear energy trap coupled dynamic response after convergence at that time step is obtained. The structural response, dynamic ice-force response, and nonlinear energy trap response at that time step are recorded.

[0063] S6. Based on the derivative of the converged dynamic ice force with respect to the relative velocity of ice and structure, identify and record the ice force negative damping excitation state at the current time step and the net negative damping state of the controlled system after adding the nonlinear energy trap. Specifically, after the current time step converges, an equivalent damping term for the ice force is constructed based on the derivative of the dynamic ice force with respect to the relative velocity of the ice and structure in the converged state. This term is then superimposed on the structure's own damping to determine whether the ice force induces a negative damping excitation effect. If the equivalent damping of the ice force weakens the structure's own damping, resulting in the structure's equivalent damping exhibiting negative damping characteristics, then the existence of a negative damping excitation state for the ice force in the current time step is recorded.

[0064] Furthermore, in the ice-force-structure-nonlinear energy trap controlled system, structural damping, ice-force equivalent damping, and nonlinear energy trap damping together constitute the total equivalent damping of the controlled system. If the extended system still exhibits negative damping characteristics after adding the nonlinear energy trap, then the controlled system is recorded as being in a net negative damping state at the current time step; if the ice-force negative damping excitation state exists but the controlled system's net negative damping state does not exist, it indicates that the nonlinear energy trap has effectively counteracted the negative damping effect of the ice force at the current time step. Figure 3 As shown.

[0065] S7. Repeat the above time step iterations until the preset total calculation time is reached, and output the structural response time history, dynamic icing force time history, nonlinear energy trap response time history, and negative damping identification results.

[0066] After each time step iterates and converges and completes data recording, it is determined whether the current calculation time has reached the preset total calculation time. If not, the process proceeds to the next time step and repeats the solution process from steps 3 to 7 above; if it has reached the preset time, the time history calculation is terminated, and the following calculation results are output: structural displacement time history, structural velocity time history, structural acceleration time history, dynamic ice force time history, nonlinear energy trap displacement time history, nonlinear energy trap relative travel time history, ice force negative damping excitation state time history, and controlled system net negative damping state time history, such as... Figure 4 As shown.

[0067] Example 2: This embodiment provides a system for solving the ice-induced structural response based on a nonlinear energy trap, including: The structural modal modeling and mode shape extraction module establishes the multi-mode dynamic equations of the structure, determines the location of ice force action and the installation location of the nonlinear energy trap, and extracts the corresponding mode shape vectors respectively. An extended dynamic equation construction module introduces nonlinear energy trap degrees of freedom into the structural multimodal dynamic equations, forming extended dynamic equations that include structural modal degrees of freedom and nonlinear energy trap degrees of freedom. The time-step prediction and ice force calculation module enters the time-step iteration. Within each time step, the Newmark-β method is used to construct the predicted displacement and predicted velocity. During the Newton iteration, based on the current ice-structure relative velocity, a piecewise ice force model based on stress rate-related ice crushing intensity is used to calculate the dynamic ice force. The piecewise ice force model calculates the stress rate parameters and current ice crushing intensity of each segment based on the current ice-structure relative velocity, and maps the current ice crushing intensity to the current contact intensity to calculate the normal ice force, friction force, and horizontal resultant force of each segment. The velocity feedback and nonlinear action term calculation module obtains the derivative of the dynamic ice force with respect to the relative velocity based on the ice-structure relative velocity in the current iteration state, and forms the ice force velocity feedback extended equivalent stiffness term from the obtained derivative. At the same time, it obtains the nonlinear action term of the nonlinear energy trap based on the response of the structure at the nonlinear energy trap installation position and the response of the nonlinear energy trap mass block. The total equivalent stiffness assembly and Newton iteration solution module assembles the basic equivalent stiffness, the velocity feedback extended equivalent stiffness term, and the nonlinear energy trap nonlinear action term into a total equivalent stiffness matrix. The total equivalent stiffness matrix is ​​used to solve for the displacement correction in the current Newton iteration step, and the displacement, velocity, and acceleration of the structure and the nonlinear energy trap are updated until the convergence condition is met, thus obtaining the coupled dynamic response after convergence in the current time step. The negative damping state identification module identifies and records the ice force negative damping excitation state at the current time step and the net negative damping state of the controlled system after adding the nonlinear energy trap, based on the derivative of the converged dynamic ice force with respect to the relative velocity of ice and structure. The iterative loop and result output module repeats the above time step iterations until the preset total calculation time is reached, and outputs the structural response time history, dynamic icing force time history, nonlinear energy trap response time history, and negative damping identification results.

[0068] The above modules can be deployed on the same device or distributed devices; the division of modules is only a functional logic description and does not limit the specific physical boundaries or implementation order.

[0069] Example 3: An electronic device is provided for running the aforementioned "method for solving the response of ice-cold structures based on a nonlinear energy trap". The electronic device includes a processor, a memory, and optional communication interfaces / display devices / input devices, etc.; the memory stores a computer program that can run on the processor, and when the processor executes the program, it implements steps S1 to S7 of the method described in Embodiment 1, specifically including but not limited to: S1. Establish the multi-mode dynamic equations of the structure, determine the location of ice force action and the installation location of the nonlinear energy trap, and extract the corresponding mode shape vectors respectively; S2. Introduce nonlinear energy trap degrees of freedom into the multi-mode dynamic equations of the structure to form extended dynamic equations that include structural modal degrees of freedom and nonlinear energy trap degrees of freedom; S3. Enter the time step iteration. In each time step, the Newmark-β method is used to construct the predicted displacement and predicted velocity. During the Newton iteration, based on the current ice-structure relative velocity, a piecewise ice force model based on stress rate-related ice crushing intensity is used to calculate the dynamic ice force. The piecewise ice force model calculates the stress rate parameters and current ice crushing intensity of each segment based on the current ice-structure relative velocity, and maps the current ice crushing intensity to the current contact intensity to calculate the normal ice force, friction force and horizontal resultant force of each segment. S4. Based on the ice-structure relative velocity in the current iteration state, obtain the derivative of the dynamic ice force with respect to the relative velocity, and form the ice force velocity feedback extended equivalent stiffness term from the obtained derivative. At the same time, based on the structure's response at the nonlinear energy trap installation location and the response of the nonlinear energy trap mass block, obtain the nonlinear action term of the nonlinear energy trap. S5. Assemble the basic equivalent stiffness, the velocity feedback extended equivalent stiffness term, and the nonlinear energy trap nonlinear action term into a total equivalent stiffness matrix. Use the total equivalent stiffness matrix to solve for the displacement correction in the current Newton iteration step, and update the displacement, velocity, and acceleration of the structure and the nonlinear energy trap until the convergence condition is met, and obtain the coupled dynamic response after convergence in the current time step. S6. Based on the derivative of the converged dynamic ice force with respect to the relative velocity of ice and structure, identify and record the ice force negative damping excitation state at the current time step and the net negative damping state of the controlled system after adding the nonlinear energy trap. S7. Repeat the above time step iterations until the preset total calculation time is reached, and output the structural response time history, dynamic icing force time history, nonlinear energy trap response time history, and negative damping identification results.

[0070] The electronic device hardware can be one of a server, personal computer, workstation, industrial controller, edge computing device, or mobile terminal; the processor can be a general-purpose CPU, GPU, NPU, FPGA, or a combination thereof; the memory can be RAM, ROM, flash memory, or disk array. The device can interact with local / remote data storage via a communication interface. The above hardware configuration does not constitute a limitation of the present invention.

[0071] Example 4: A computer-readable storage medium storing a computer program, which, when run on a processor of an electronic device, causes the program to execute the method steps S1 to S7 described in Embodiment 1; the storage medium may be a disk, optical disk, flash memory, solid-state drive, read-only memory, random access memory, or any combination of the above media.

[0072] Those skilled in the art will understand that the modules or steps described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, which can then be stored in a storage device for execution by a computer device. Alternatively, they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. This disclosure is not limited to any particular combination of hardware and software.

[0073] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0074] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for solving the ice-induced structural response based on a nonlinear energy trap, characterized in that, Includes the following steps: Establish the multi-mode dynamic equations of the structure, determine the location of ice force action and the installation location of the nonlinear energy trap, and extract the corresponding mode shape vectors respectively; By introducing nonlinear energy trap degrees of freedom into the structural multimodal dynamic equations, an extended dynamic equations containing structural modal degrees of freedom and nonlinear energy trap degrees of freedom are formed. Entering the time step iteration, the Newmark-β method is used to construct the predicted displacement and predicted velocity in each time step, and the dynamic ice force is calculated using a piecewise ice force model based on stress rate-related ice crushing intensity during the Newton iteration process, according to the current ice-structure relative velocity. The segmented ice force model calculates the stress rate parameters and current ice crushing intensity of each segment based on the current ice-structure relative velocity, and maps the current ice crushing intensity to the current contact intensity to calculate the normal ice force, friction force and horizontal resultant force of each segment; The derivative of the dynamic ice force with respect to the relative velocity is obtained from the ice-structure relative velocity under the current iteration state, and the ice force velocity feedback extended equivalent stiffness term is formed from the obtained derivative. At the same time, the nonlinear action term of the nonlinear energy trap is obtained from the response of the structure at the nonlinear energy trap installation position and the response of the nonlinear energy trap mass block. The basic equivalent stiffness, the velocity feedback extended equivalent stiffness term, and the nonlinear energy trap nonlinear action term are assembled into a total equivalent stiffness matrix. The total equivalent stiffness matrix is ​​used to solve for the displacement correction in the current Newton iteration step, and the displacement, velocity, and acceleration of the structure and the nonlinear energy trap are updated until the convergence condition is met, thus obtaining the coupled dynamic response after convergence in the current time step. Based on the derivative of the converged dynamic ice force with respect to the relative velocity of ice and structure, identify and record the ice force negative damping excitation state at the current time step and the net negative damping state of the controlled system after adding the nonlinear energy trap. Repeat the above time step iterations until the preset total calculation time is reached, and output the structural response time history, dynamic icing force time history, nonlinear energy trap response time history, and negative damping identification results.

2. The method for solving the ice-induced structural response based on a nonlinear energy trap according to claim 1, characterized in that, The method for assembling the total equivalent stiffness matrix includes: Construct the Newmark basic equivalent stiffness matrix: ； in, , , These are the extended mass matrix, extended damping matrix, and extended stiffness matrix, which contain structural modal degrees of freedom and nonlinear energy trap degrees of freedom, respectively. and For the integration parameters of the Newmark-β method, For time step; Based on the ice-structure relative velocity in the current Newton iteration step The derivative of the dynamic ice force with respect to the relative velocity of the ice and structure is obtained using the central difference method: ； in, To preset the relative velocity disturbance, For dynamic ice force; the derivative is... Converted to the extended equivalent stiffness term of ice force velocity feedback in extended degree-of-freedom space: ； in, This is the mode shape vector of the ice force at the location where the ice force acts; Construct the relative response vector of the nonlinear energy trap: ； in, This is the mode shape vector at the mounting point corresponding to the nonlinear energy trap installation location; According to the extended displacement vector and extended velocity vector The relative displacement and relative velocity of the nonlinear energy trap are obtained: ； ； The velocity feedback extended equivalent stiffness term and the nonlinear energy trap nonlinear action term are combined to construct the ice force-nonlinear energy trap additional equivalent stiffness matrix: ； in, The stiffness coefficient of the nonlinear energy trap. The damping coefficient of the nonlinear energy trap; The Newmark basic equivalent stiffness matrix and the ice force-nonlinear energy trap additional equivalent stiffness matrix are assembled together to form the total equivalent stiffness matrix: 。 3. The method for solving the ice-induced structural response based on a nonlinear energy trap according to claim 1, characterized in that, In the segmented ice force model, the contact area of ​​the structure on the ice-facing side is divided into multiple calculation blocks along the circumferential direction. Each computational block is based on the current ice-structure relative velocity. Calculate its radial relative velocity: ； in, Let be the central angle of the j-th computational block, and be the ice crushing intensity of the j-th computational block. Determined according to the following segmentation method: ； ； Calculated based on the current ice crushing intensity. Contact stress of each calculation block: ； And the normal ice force is obtained based on the area of ​​the calculated block: ； The frictional force is obtained from the normal ice force: ； No. The horizontal component of the force along the direction of ice velocity in each calculation block: ； in, The diameter of the structure. Because the ice is thick, Let be the ice-structure friction coefficient; sum the horizontal components of the forces across all calculated blocks, and obtain the total dynamic ice force based on structural symmetry: ； in, To calculate the number of blocks.

4. The method for solving the ice-induced structural response based on a nonlinear energy trap according to claim 1, characterized in that, Methods for identifying negative damping include: According to ice speed Calculate the structural modal velocities at the locations where ice forces interact, and the relative velocities between the ice and the structure. ,in, The structural modal velocity vector, This represents the ice force mode shape vector corresponding to the location where the ice force acts; the dynamic ice force is expressed as a function of the relative velocity between the ice and the structure. And calculate the derivative of the dynamic ice force with respect to the relative velocity of the ice and structure near the convergence state at the current time step. ; Construct the ice force equivalent damping matrix based on the derivative. The equivalent damping matrix is ​​obtained by superimposing the ice force equivalent damping matrix with the structural damping matrix. When the equivalent damping matrix has negative damping characteristics, or the target mode satisfies When it is determined that the current time step exists in the state of ice force negative damping excitation, where For the first Step structure modal damping, The mode shape vector corresponding to the position where the ice force acts is at the th position. Components in the first mode; In an extended degree-of-freedom space containing the nonlinear energy trap degree of freedom, construct the nonlinear energy trap damping matrix. Ice force velocity feedback extended damping matrix and the structural extended damping matrix The total equivalent damping matrix of the ice force-structure-nonlinear energy trap controlled system is obtained as follows: When the total equivalent damping matrix of the controlled system has negative damping characteristics, or has an extended velocity vector Make At that time, it was determined that the system after adding the nonlinear energy trap was still in a state of net negative damping.

5. The method for solving the ice-induced structural response based on a nonlinear energy trap according to claim 1, characterized in that, When the relative velocity between the ice and the structure is in a preset near-zero velocity range, an ice force smoothing activation function is introduced. The original ice force obtained from the piecewise ice force model is multiplied by the ice force smoothing activation function, so that the ice force transitions continuously from zero to the original ice force during the initial contact stage. The ice force smoothing activation function is: ； ； in, The relative velocity between the ice and the structure. The preset smoothing speed threshold.

6. The method for solving the ice-induced structural response based on a nonlinear energy trap according to claim 1, characterized in that, When establishing the multimodal dynamic equations of the structure, the first few modes of the structure are selected for calculation. The structural modal mass matrix, structural modal damping matrix, and structural modal stiffness matrix are established based on the natural frequencies and mode shape data of the structure. The ice force mode shape vector corresponding to the ice force application location is extracted from the structural mode shape data based on the ice force application height. The installation point mode shape vector corresponding to the installation location of the nonlinear energy trap is extracted based on the installation height of the nonlinear energy trap.

7. The method for solving the ice-induced structural response based on a nonlinear energy trap according to claim 1, characterized in that, The output negative damping identification results include the ice force negative damping excitation state time history and the controlled system net negative damping state time history; if the ice force negative damping excitation state exists but the controlled system net negative damping state does not exist, it is determined that the nonlinear energy trap has canceled the ice force negative damping effect in the current time step; the output structural response time history includes the structural displacement time history, structural velocity time history and structural acceleration time history, and the output nonlinear energy trap response time history includes the nonlinear energy trap displacement time history and the nonlinear energy trap relative travel time history.

8. A system for solving the ice-induced structural response based on a nonlinear energy trap, characterized in that, include: The structural modal modeling and mode shape extraction module establishes the multi-mode dynamic equations of the structure, determines the location of ice force action and the installation location of the nonlinear energy trap, and extracts the corresponding mode shape vectors respectively. An extended dynamic equation construction module introduces nonlinear energy trap degrees of freedom into the structural multimodal dynamic equations, forming extended dynamic equations that include structural modal degrees of freedom and nonlinear energy trap degrees of freedom. The time step prediction and ice force calculation module enters the time step iteration. In each time step, the Newmark-β method is used to construct the predicted displacement and predicted velocity. During the Newton iteration, the dynamic ice force is calculated based on the current ice-structure relative velocity using a piecewise ice force model based on stress rate-related ice crushing strength. The segmented ice force model calculates the stress rate parameters and current ice crushing intensity of each segment based on the current ice-structure relative velocity, and maps the current ice crushing intensity to the current contact intensity to calculate the normal ice force, friction force and horizontal resultant force of each segment; The velocity feedback and nonlinear action term calculation module obtains the derivative of the dynamic ice force with respect to the relative velocity based on the ice-structure relative velocity in the current iteration state, and forms the ice force velocity feedback extended equivalent stiffness term from the obtained derivative. At the same time, it obtains the nonlinear action term of the nonlinear energy trap based on the response of the structure at the nonlinear energy trap installation position and the response of the nonlinear energy trap mass block. The total equivalent stiffness assembly and Newton iteration solution module assembles the basic equivalent stiffness, the velocity feedback extended equivalent stiffness term, and the nonlinear energy trap nonlinear action term into a total equivalent stiffness matrix. The total equivalent stiffness matrix is ​​used to solve for the displacement correction in the current Newton iteration step, and the displacement, velocity, and acceleration of the structure and the nonlinear energy trap are updated until the convergence condition is met, thus obtaining the coupled dynamic response after convergence in the current time step. The negative damping state identification module identifies and records the ice force negative damping excitation state at the current time step and the net negative damping state of the controlled system after adding the nonlinear energy trap, based on the derivative of the converged dynamic ice force with respect to the relative velocity of ice and structure. The iterative loop and result output module repeats the above time step iterations until the preset total calculation time is reached, and outputs the structural response time history, dynamic icing force time history, nonlinear energy trap response time history, and negative damping identification results.

9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and running thereon, characterized in that, When the processor executes the program, it implements the ice-induced structural response solution method based on a nonlinear energy trap as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the ice-induced structural response solution method based on a nonlinear energy trap as described in any one of claims 1-7.

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