A method for analyzing the hydroelastic response of a floating pier considering the combined effects of multiple loads

Abstract

This application discloses a method for analyzing the hydroelastic response of a floating pier that takes into account the combined effects of multiple loads. This method relates to the field of floating piers. The method first determines the elastic modal information of the floating pier through modal analysis. Then, based on the vehicle type on the floating pier, the axle loads of each vehicle axle are determined. The total vehicle load on the floating pier from all vehicles under the elastic modal conditions is calculated by combining the real-time center of gravity of the vehicles and the elastic modal information of the floating pier. The hydroelastic response analysis results of the floating pier are obtained by solving the three-dimensional time-domain hydroelastic motion equations of the floating pier in combination with the total wave loads on the floating pier. This method can consider the combined effects of vehicle loads and wave loads, and can more accurately predict the hydroelastic response analysis results of the floating pier during operation, including motion response, profile loads, and connector loads. The response analysis has high accuracy and precision.

Description

Technical Field

[0001] The present application relates to the field of floating piers, and in particular to a method for analyzing the hydroelastic response of floating piers taking into account the combined effects of multiple loads. Background Art

[0002] Floating piers play a vital role in coastal mudflat development, offshore island and reef construction, and emergency rescue efforts. They provide a fast and efficient transportation channel for large-scale machinery transportation, material supply, and personnel movement. Floating piers are typically composed of multiple connected sections and can be constructed in varying lengths to meet specific needs.

[0003] The design and application of floating piers requires calculation of their hydroelastic response under loads to assess the inter-segment connection system and local strength of the segments. Currently, hydroelastic analysis of floating piers under wave action is a relatively mature technique for determining their hydroelastic response. However, in reality, floating piers must withstand not only wave loads but also the impact of vehicles passing over them. Therefore, existing analysis methods that only consider wave loads result in low accuracy and precision in hydroelastic response analysis. Summary of the Invention

[0004] In response to the above-mentioned problems and technical needs, this application proposes a method for analyzing the hydroelastic response of a floating pier taking into account the combined effects of multiple loads. The technical solution of this application is as follows:

[0005] A method for analyzing the hydroelastic response of a floating pier taking into account the combined action of multiple loads is provided. The method comprises:

[0006] A finite element model of the floating pier is constructed based on the structural parameters of the floating pier to perform modal analysis and determine the elastic modal information of the floating pier;

[0007] For each vehicle on the floating trestle, the axle load of each wheel axle of the vehicle is determined according to the vehicle type. Combined with the center of gravity position of the vehicle at any time t and the elastic modal information of the floating trestle, the vehicle load of the vehicle on the bridge section at the time t in the elastic mode is calculated; the total vehicle load F of all vehicles on the floating trestle at the time t in the elastic mode is obtained. Ve (t);

[0008] Calculate the total wave load F(t) on the floating pier at time t based on the elastic modal information of the floating pier;

[0009] The total wave load F(t) and the total vehicle load F Ve(t) Substitute into the three-dimensional time-domain hydroelastic motion equation of the floating pier considering the combined action of moving load and wave load Obtain the hydroelastic response analysis results of the floating pier at time t;

[0010] Among them, the generalized structural mass matrix [A] is the sum of the structural mass matrix of the floating pier and the mass of all vehicles passing on the floating pier at time t; [Α ∞ ] is the generalized added mass matrix at infinite frequency, [b] is the generalized structural damping matrix, K(t-τ) is the delay function, and q(t) is the principal coordinate response of the floating pier at time t.

[0011] A further technical solution is to calculate the vehicle load of each passing vehicle on the bridge section at time t in the elastic mode, including:

[0012] Determine the axle distribution structure of the vehicle according to the vehicle type of the vehicle, and determine the real-time position of each axle of the vehicle at any time t according to the center of gravity position of the vehicle at any time t in combination with the axle distribution structure of the vehicle;

[0013] According to the real-time position of each axle of the vehicle at time t, the position of the wheels connected to both ends of the axle is determined as the contact position of the vehicle with the floating pier at time t;

[0014] According to the axle load of each wheel axle of the through-car vehicle and the real-time position of each wheel axle at time t, the vehicle load of the through-car vehicle on the bridge section at time t in the rigid body degree of freedom is calculated;

[0015] According to the vehicle load of the conventional vehicle on the bridge section in the rigid body degree of freedom at time t and the elastic modal information of the contact position between the floating trestle and the conventional vehicle at time t, the vehicle load of the conventional vehicle on the bridge section of the floating trestle in the elastic mode at time t is obtained.

[0016] A further technical solution is to calculate the vehicle load of the through-car vehicle on the bridge section at time t in the rigid body degree of freedom, including:

[0017] According to the real-time position of each wheel axle of the vehicle at time t, the longitudinal distance between the wheel axle center position and the center of gravity of the bridge section along the length direction of the bridge section and the transverse distance between the wheel axle center position and the median longitudinal line of the bridge section along the width direction of the bridge section are determined;

[0018] According to the axle load of each wheel axle of the through-car vehicle, and the longitudinal and lateral distances between each wheel axle and the center of gravity of the bridge section at time t, the vehicle load of the through-car vehicle on the bridge section at time t in the rigid body degree of freedom is calculated, including the vertical load along the vertical direction, the longitudinal moment along the length direction of the bridge section, and the lateral moment along the width direction of the bridge section.

[0019] Its further technical solution is that the vertical load of the vehicle on the bridge section in the vertical direction under the rigid body freedom at time t is

[0020] The longitudinal moment of the vehicle on the bridge section along the length direction of the bridge section at time t under the rigid body degree of freedom is:

[0021] The lateral moment of the vehicle on the bridge section along the width direction of the bridge section at time t in the rigid body degree of freedom is:

[0022] Among them, m i is the axle load of any i-th axle of the through-car, g is the acceleration of gravity, N is the total number of axles of the through-car located on the bridge section, l i (t) is the longitudinal distance between the i-th wheel axle and the center of gravity of the bridge section at time t, d Vi (t) is the lateral distance between the i-th axle and the center of gravity of the bridge section at time t.

[0023] A further technical solution is to calculate the total wave load F(t) received by the floating pier at time t based on the elastic modal information of the floating pier, including:

[0024] According to the wave parameters of the sea area where the floating pier is located at time t and the structural parameters of the floating pier, the instantaneous wet surface S of the floating pier at time t is determined. b (t);

[0025] According to the instantaneous wet surface S of the floating pier at time t b (t) Calculate the nonlinear generalized incident wave force F on the floating pier at time t I (t) and the nonlinear generalized hydrostatic restoring force F R (t);

[0026] The total wave load on the floating pier at time t is calculated as {F(t)}={F I (t)}+{F D (t)}+{F R (t)}+{G(t)}; where F D (t) is the generalized diffraction wave force on the floating pier at time t, and G(t) is the generalized gravity on the floating pier at time t.

[0027] A further technical solution is that the nonlinear generalized incident wave force of the floating pier at the rth order mode of the floating pier at time t is Where ρ is the fluid density in the sea area where the floating pier is located, n is the instantaneous wet surface S of the floating pier at time t b(t) is the direction vector, φ0 is the incident wave velocity potential, u r is the vibration shape of the rth mode of the floating pier.

[0028] A further technical solution is that the nonlinear generalized hydrostatic restoring force of the floating pier at the rth order mode of the floating pier at time t is Where ρ is the fluid density in the sea area where the floating pier is located, g is the acceleration of gravity, and n is the instantaneous wet surface S of the floating pier at time t. b (t) direction vector, u r is the vibration shape of the rth mode of the floating pier, w k is the vertical displacement component of the floating pier under the kth mode, and m is the total number of elastic modes of the floating pier.

[0029] A further technical solution is to establish the connecting parts between the bridge sections of the floating pier using equivalent beam-spring units when establishing the finite element model of the floating pier. The elastic modal information of the floating pier obtained by modal analysis includes the node displacement, node stress, key section load and connector load under each elastic mode.

[0030] A further technical solution is to obtain the hydroelastic response analysis results of the floating pier at time t, including:

[0031] The three-dimensional time-domain hydroelastic motion equations of the floating pier are solved to obtain the principal coordinate responses q(t) of each mode of the floating pier. The hydroelastic response analysis results of the floating pier at time t are calculated based on the principal coordinate responses q(t) of each mode and the elastic modal information of the floating pier, including the motion response of the floating pier, key section loads, and connector loads.

[0032] The beneficial technical effects of this application are:

[0033] The present application discloses a method for analyzing the hydroelastic response of a floating pier taking into account the combined effects of multiple loads. The method calculates the vehicle loads on the floating pier at different times based on the axle loads and real-time positions of the vehicles passing through the floating pier. Combined with the wave loads on the floating pier, the method uses a three-dimensional time-domain hydroelastic motion equation to perform response analysis. This method can consider the combined effects of vehicle loads and wave loads and can more accurately predict the hydroelastic response analysis results of the floating pier during operation, including motion response, profile loads, and connector loads. The response analysis has high accuracy and precision.

[0034] This method can more accurately characterize the wave loads on the floating pier by considering the instantaneous wet surface changes. By considering the combined effects of factors such as wave load, vehicle load, gravity and elastic deformation of the floating pier on the hydroelastic response of the floating pier, the calculation accuracy of the hydroelastic response of the floating pier is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of a method for analyzing the hydroelastic response of a floating pier according to an embodiment of the present application.

[0036] Figure 2 It is a structural diagram of a floating pier.

[0037] Figure 3 It is a side view schematic diagram of a vehicle being carried on a bridge section of a floating trestle.

[0038] Figure 4 It is a side view schematic diagram of a vehicle being carried on a bridge section of a floating trestle.

[0039] Figure 5 The figure is a result diagram of the vertical displacement of the floating trestle obtained by using the hydroelastic response analysis method of the floating trestle of the present application when a vehicle traveling on the floating trestle at different speeds in an example. DETAILED DESCRIPTION

[0040] The specific implementation of this application will be further described below with reference to the accompanying drawings.

[0041] This application discloses a method for analyzing the hydroelastic response of a floating pier taking into account the combined effects of multiple loads. Figure 1 The process diagram shown in FIG. 1 includes the following steps:

[0042] Step 1: construct a finite element model of the floating pier according to the structural parameters of the floating pier, perform modal analysis, and determine the elastic modal information of the floating pier.

[0043] The structural parameters of a floating pier include the number of bridge sections, the specifications of each bridge section, and the mooring system. Figure 2 As shown in the structural diagram, a floating pier consists of several bridge sections 1, which are connected in sequence along their length to form a shore-connected channel, serving as the main structure of the floating pier. The bridge sections at one end of the floating pier are located on the shore, while the bridge sections at the other end are located in the sea. The specifications of each bridge section include its length and width. The bridge sections are connected by connectors 2. The floating pier's mooring system primarily includes anchors 3 for positioning and cables 4 for connecting the bridge sections to the anchors 3.

[0044] When building the finite element model of the floating pier, the connectors 2 between the bridge sections were constructed using equivalent beam-spring elements. Modal analysis of the finite element model then revealed elastic modal information, including nodal displacements, nodal stresses, critical section loads, and connector loads under each elastic mode. The modal analysis also considered the influence of the stiffness of the inter-section connectors.

[0045] Step 2: For each vehicle on the floating trestle, determine the axle load of each axle of the vehicle according to the vehicle type. Combined with the center of gravity position of the vehicle at any time t and the elastic modal information of the floating trestle, calculate the vehicle load of the vehicle on the bridge section at time t in the elastic modal. The total vehicle load F of all vehicles on the floating trestle at time t in the elastic modal is obtained. Ve (t).

[0046] The floating trestle also houses several vehicles 5, which travel on the shore-connecting channel formed by the connected bridge sections. Each vehicle 5 includes several axles 51, with wheels 52 connected to each axle 51 on both sides. At any given moment, the wheels connected to all axles of a vehicle 5 are on the same bridge section 1, meaning that the vehicle 5 is completely located on one bridge section 1. Alternatively, the wheels connected to all axles of a vehicle 5 are located on two adjacent bridge sections 1, meaning that the vehicle 5 is located at the connection point between two bridges. Figure 2 Taking the example of a vehicle 5 on a floating trestle and the vehicle 5 being completely located on one bridge section 1, the side view of the vehicle 5 on the bridge section is as follows: Figure 3 As shown, the top view diagram is as follows Figure 4 As shown, it should be noted that Figure 2-Figure 4 It is for illustration only and does not represent the actual ratio of vehicles to bridge sections.

[0047] According to the vehicle type of the vehicle, the number of axles and the axle distribution structure of the vehicle can be determined and a dynamic calculation model of the vehicle can be established. Based on the dynamic calculation model, the axle load of each axle, that is, the vehicle weight shared by the axle, can be determined. The axle distribution structure and dynamic calculation model of the same vehicle type are similar and can be configured in advance. For example, common vehicle types include cars, buses, trucks and trailers. Cars, buses and trucks generally have two axles in the front and rear, but the distance between the two axles varies for different vehicle types. Trailers usually have 5 axles from front to back, such as Figure 2-Figure 4 Taking the vehicle type of the common vehicle 5 as a trailer as an example, the axle distribution structure and dynamic calculation model of different common vehicle types can refer to existing relevant models, and the axle load of each axle obtained by further calculation can refer to existing axle load calculation methods, which will not be repeated in this application.

[0048] The axle distribution structure of a through-car vehicle indicates the relationship between each axle of the through-car vehicle and the center of gravity of the through-car vehicle. Therefore, after determining the center of gravity position of the through-car vehicle and its axle distribution structure at any time t, the real-time position of each axle of the through-car vehicle at time t can be determined. Since the length of each axle is fixed and known, the real-time position of each axle at time t includes the center position of the axle and the positions of the wheels connected to both ends of the axle. The position of the wheel is the contact position of the through-car vehicle with the floating pier at time t. Therefore, the contact position of the through-car vehicle with the floating pier at time t can be determined.

[0049] On the other hand, based on the axle load of each wheel axle of the vehicle and the real-time position of each wheel axle at time t, the vehicle load of the vehicle on the bridge section at time t in the rigid body degree of freedom is calculated, including:

[0050] First, the longitudinal and transverse distances between the axle center position and the center of gravity of the bridge section are determined based on the real-time position of each axle of the vehicle at time t, including determining the longitudinal distance l between the axle center position of any i-th axle and the center of gravity of the bridge section along the length direction of the bridge section. i (t), please refer to Figure 3 And determine the transverse distance d between the center position of any i-th axle and the middle longitudinal line of the bridge section along the width direction of the bridge section Vi (t), please refer to Figure 4 .

[0051] Then, based on the axle load of each wheel axle of the through-car vehicle and the longitudinal and lateral distances between each wheel axle and the center of gravity of the bridge section at time t, the vehicle load of the through-car vehicle on the bridge section at time t in the rigid body degree of freedom is calculated. The obtained vehicle load includes the vertical load of the through-car vehicle on the bridge section in the vertical direction, the longitudinal moment along the length direction of the bridge section, and the lateral moment along the width direction of the bridge section, including:

[0052] Determine the vertical load of the vehicle on the bridge section in the vertical direction under the rigid body freedom at time t:

[0053] Determine the longitudinal moment of the vehicle on the bridge section along the length direction of the bridge section under the rigid body freedom at time t:

[0054] Determine the lateral moment of the vehicle on the bridge section along the width direction of the bridge section under the rigid body freedom at time t:

[0055] Among them, m i is the axle load of any i-th wheel axle of the vehicle, g is the acceleration of gravity, l i(t) is the longitudinal distance between the i-th wheel axle and the center of gravity of the bridge section at time t, d Vi (t) is the lateral distance between the i-th axle and the center of gravity of the bridge section at time t. N is the total number of axles of vehicles on the bridge section.

[0056] In one case, all axles of the through-carriage vehicle are located on the same bridge section. The total number N of axles of the through-carriage vehicle located on the bridge section is the total number of axles contained in the through-carriage vehicle. The vehicle load of the through-carriage vehicle on one bridge section is calculated accordingly.

[0057] In another case, when the through-car vehicle travels to the connection of two bridge sections, all the axles of the through-car vehicle are located on two adjacent bridge sections. Then the through-car vehicle is located on two bridge sections respectively, and the total number N of axles of the through-car vehicle located on each bridge section is the partial axles included in the through-car vehicle. For example, in 3 and Figure 4 In the example of , the three wheel axles at the front of the through-car 5 are located on one bridge section, and the two wheel axles at the rear are located on another bridge section. In this case, the vehicle loads of the through-car 5 on the two bridge sections are calculated accordingly.

[0058] Regardless of the situation, after calculating the vehicle load of the through-car vehicle on the bridge section at time t under the rigid body degrees of freedom and determining the contact position of the through-car vehicle with the floating trestle at time t, the vehicle load of the through-car vehicle on the bridge section of the floating trestle at time t under the elastic mode information at the contact position between the floating trestle and the through-car vehicle can be calculated in combination with the vehicle load under the rigid body degrees of freedom.

[0059] The vehicle load of each passing vehicle on the bridge section of the floating trestle in the elastic mode at time t can be calculated separately according to the above method. Then, the vehicle loads of all passing vehicles can be combined to obtain the total vehicle load F of all passing vehicles on the floating trestle in the elastic mode at time t. Ve (t).

[0060] Step 3: Calculate the total wave load F(t) received by the floating pier at time t based on the elastic modal information of the floating pier.

[0061] In one embodiment, the total wave load F(t) received by the floating pier is different from the method used in the traditional response analysis method to calculate the wave load received by the floating pier. This embodiment also takes into account the change of the instantaneous wetted surface of the floating pier to improve the accuracy of the total wave load, thereby improving the accuracy of the subsequent response analysis. In this embodiment, the total wave load F(t) received by the floating pier includes four categories, namely: the generalized diffraction wave force F(t) received by the floating pier at time t; D(t), the generalized gravity G(t) of the floating pier at time t, and the nonlinear generalized incident wave force F of the floating pier at time t I (t), the nonlinear generalized hydrostatic restoring force F of the floating pier at time t R (t). That is, the total wave load on the floating pier at time t can be expressed as {F(t)}={F I (t)}+{F D (t)}+{F R (t)}+{G(t)}. Among them, the generalized diffraction wave force F that the floating pier receives at time t is D (t) is obtained by superposition of the frequency domain results of the generalized diffraction wave force. The generalized gravity G(t) of the floating pier at time t is obtained from the generalized mass and gravitational acceleration of the floating pier. The generalized mass of the floating pier can be obtained during the modal analysis of the floating structure.

[0062] The generalized incident wave force and generalized hydrostatic restoring force on the floating pier are no longer calculated using the average wetted surface of the floating pier as in the traditional method, but are calculated based on the instantaneous wetted surface S of the floating pier at time t. b (t) to calculate, so that the nonlinear force can be calculated, including:

[0063] According to the wave parameters of the sea area where the floating pier is located at time t and the structural parameters of the floating pier, the instantaneous wet surface S of the floating pier at time t is determined. b (t), instantaneous wet surface S b The specific calculation method of (t) can refer to the existing method, which will not be described in detail in this application. b (t), according to the instantaneous wet surface S of the floating pier at time t b (t) Calculate the nonlinear generalized incident wave force F on the floating pier at time t I (t) and the nonlinear generalized hydrostatic restoring force F R (t):

[0064] Nonlinear generalized incident wave force on a floating pier at time t under the rth mode of the floating pier The nonlinear generalized hydrostatic restoring force of the floating pier at time t in the rth mode of the floating pier

[0065] Where ρ is the fluid density in the sea area where the floating pier is located, g is the acceleration due to gravity, and n is the instantaneous wetted surface S of the floating pier at time t. b (t) is the direction vector, φ0 is the incident wave velocity potential, u r is the vibration shape of the rth mode of the floating pier. φ0 is the incident wave velocity potential, w kis the vertical displacement component of the floating pier under the kth mode, and m is the total number of elastic modes of the floating pier.

[0066] Step 4: The total wave load F(t) and the total vehicle load F Ve (t) Substitute into the three-dimensional time-domain hydroelastic motion equation of the floating pier considering the combined action of moving load and wave load:

[0067]

[0068] Among them, the generalized structural mass matrix [a] is the sum of the structural mass matrix of the floating pier and the mass of all vehicles passing on the floating pier at time t. The structural mass matrix of the floating pier can be calculated using the finite element method.

[0069] [Α ∞ ] is the generalized added mass matrix at infinite frequency, [b] is the generalized structural damping matrix, K(t-τ) is the delay function. q(t) is the principal coordinate response of the floating pier at time t, is the first derivative of q(t), is the second derivative of q(t).

[0070] Solving the three-dimensional time-domain hydroelastic motion equations for the floating pier yields the hydroelastic response analysis results for the floating pier under the combined action of moving and wave loads at time t. This involves first obtaining the principal coordinate responses q(t) of each mode of the floating pier. Then, using these principal coordinate responses q(t) and the elastic modal information of the floating pier, the hydroelastic response analysis results for the floating pier at time t are calculated, including the floating pier's motion response, key section loads, and connector loads.

[0071] The hydroelastic response analysis method of the present application can simultaneously consider the combined effects of wave loads and the moving loads of vehicles on the floating pier on the hydroelastic response of the floating pier, and improves the accuracy of wave loads by considering the instantaneous wetted surface changes. In one example, when a vehicle moves on the floating pier at three different speeds V, the vertical displacement results of the floating pier's motion response are as follows: Figure 5 shown.

[0072] The above description is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and variations directly derived or imagined by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the scope of protection of the present application.

Claims

1. A method for analyzing the hydroelastic response of a floating pier taking into account the combined effects of multiple loads, characterized in that: The floating pier hydroelastic response analysis method comprises: Constructing a finite element model of the floating pier based on the structural parameters of the floating pier, performing modal analysis, and determining elastic modal information of the floating pier; For each vehicle on the floating trestle, the axle load of each wheel axle of the vehicle is determined according to the vehicle type. Combined with the center of gravity position of the vehicle at any time t and the elastic modal information of the floating trestle, the vehicle load of the vehicle on the bridge section at the time t in the elastic mode is calculated; the total vehicle load F of all vehicles on the floating trestle at the time t in the elastic mode is obtained. Ve (t); Calculating the total wave load F(t) received by the floating pier at time t according to the elastic modal information of the floating pier; The total wave load F(t) and the total vehicle load F Ve (t) Substitute into the three-dimensional time-domain hydroelastic motion equation of the floating pier considering the combined action of moving load and wave load Obtaining a hydroelastic response analysis result of the floating pier at time t; Wherein, the generalized structural mass matrix [A] is the sum of the structural mass matrix of the floating trestle and the mass of all vehicles passing on the floating trestle at time t; [A ∞ ] is the generalized added mass matrix at infinite frequency, [b] is the generalized structural damping matrix, K(t-τ) is the delay function, and q(t) is the principal coordinate response of the floating pier at time t.

2. The method for analyzing the hydroelastic response of a floating pier according to claim 1, characterized in that: The calculated vehicle loads of each through-car vehicle on the bridge section at time t in the elastic mode include: Determining the axle distribution structure of the vehicle according to the vehicle type of the vehicle, and determining the real-time position of each axle of the vehicle at any time t according to the center of gravity position of the vehicle at any time t in combination with the axle distribution structure of the vehicle; Determining the positions of the wheels connected at both ends of the axles according to the real-time positions of the axles of the vehicle at time t as the contact positions of the vehicle with the floating pier at time t; Calculate the vehicle load of the vehicle on the bridge section at time t in the rigid body degree of freedom according to the axle load of each axle of the vehicle and the real-time position of each axle at time t; Based on the vehicle load of the through-car vehicle on the bridge section in which it is located in the rigid body degree of freedom at time t, and the elastic modal information of the contact position between the floating trestle and the through-car vehicle at time t, the vehicle load of the through-car vehicle on the bridge section of the floating trestle in the elastic mode at time t is obtained.

3. The method for analyzing the hydroelastic response of a floating pier according to claim 2, characterized in that: The calculation of the vehicle load of the through-car vehicle on the bridge section at time t under the rigid body degree of freedom includes: Determine, based on the real-time position of each wheel axle of the vehicle at time t, the longitudinal distance between the wheel axle center position and the center of gravity of the bridge section along the length direction of the bridge section, and the transverse distance between the wheel axle center position and the median longitudinal line of the bridge section along the width direction of the bridge section; According to the axle load of each wheel axle of the through-carrying vehicle, and the longitudinal and lateral distances between each wheel axle and the center of gravity of the bridge section at time t, the vehicle load of the through-carrying vehicle on the bridge section at time t in the rigid body degree of freedom is calculated, including the vertical load along the vertical direction, the longitudinal moment along the length direction of the bridge section, and the lateral moment along the width direction of the bridge section.

4. The method for analyzing the hydroelastic response of a floating pier according to claim 3, wherein: The vertical load of the vehicle on the bridge section in the rigid body degree of freedom at time t is The longitudinal moment of the vehicle on the bridge section along the length direction of the bridge section at time t under the rigid body degree of freedom is The lateral moment of the vehicle on the bridge section along the width direction of the bridge section at time t under the rigid body degree of freedom is Among them, m i is the axle load of any i-th axle of the vehicle, g is the acceleration of gravity, N is the total number of axles of the vehicle located on the bridge section, l i (t) is the longitudinal distance between the i-th wheel axle and the center of gravity of the bridge section at time t, d Vi (t) is the lateral distance between the i-th axle and the center of gravity of the bridge section at time t.

5. The method for analyzing the hydroelastic response of a floating pier according to claim 1, wherein: Calculating the total wave load F(t) received by the floating pier at time t according to the elastic modal information of the floating pier includes: The instantaneous wetted surface S of the floating pier at time t is determined based on the wave parameters of the sea area where the floating pier is located at time t and the structural parameters of the floating pier. b (t); According to the instantaneous wet surface S of the floating pier at time t b (t) Calculate the nonlinear generalized incident wave force F of the floating pier at time t I (t) and the nonlinear generalized hydrostatic restoring force F R (t); The total wave load {F(t)} received by the floating pier at time t is calculated to be {F I (t)}+{F D (t)}+{F R (t)}+{G(t)}; where F D (t) is the generalized diffraction wave force on the floating pier at time t, and G(t) is the generalized gravity on the floating pier at time t.

6. The method for analyzing the hydroelastic response of a floating pier according to claim 5, characterized in that: The nonlinear generalized incident wave force of the floating pier under the r-th order mode of the floating pier at time t Wherein, ρ is the fluid density of the sea area where the floating pier is located, n is the instantaneous wet surface S of the floating pier at time t b (t) is the direction vector, φ0 is the incident wave velocity potential, u r is the vibration shape of the rth mode of the floating pier.

7. The method for analyzing the hydroelastic response of a floating pier according to claim 5, characterized in that: The nonlinear generalized hydrostatic restoring force of the floating pier at time t in the r-th order mode of the floating pier Wherein, ρ is the fluid density in the sea area where the floating pier is located, g is the acceleration of gravity, and n is the instantaneous wetted surface S of the floating pier at time t. b (t) direction vector, u r is the vibration shape of the rth order mode of the floating pier, w k is the vertical displacement component of the floating pier in the kth mode, and m is the total number of elastic modes of the floating pier.

8. The method for analyzing the hydroelastic response of a floating pier according to claim 1, wherein: When establishing a finite element model of a floating pier, the connectors between the bridge sections of the floating pier are established using equivalent beam-spring units. The elastic modal information of the floating pier obtained through modal analysis includes node displacements, node stresses, key section loads, and connector loads under each elastic mode.

9. The method for analyzing the hydroelastic response of a floating pier according to claim 8, characterized in that: The hydroelastic response analysis results of the floating pier at time t include: The three-dimensional time-domain hydroelastic motion equation of the floating pier is solved to obtain the principal coordinate response q(t) of each mode of the floating pier. The hydroelastic response analysis results of the floating pier at time t are calculated using the principal coordinate response q(t) of each mode and the elastic modal information of the floating pier, including the motion response, key section loads, and connector loads of the floating pier.

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