A test measurement system for wave force of a pile cap structure based on inertial force influence
Patent Information
- Application Number
- CN202310262189.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-03-17
- Publication Date
- 2026-09-11
- Estimated Expiration
- 2043-03-17
AI Technical Summary
然而,上述测量方法的试验结果均未考虑结构物自身惯性力部分的影响,致使结构物所受波浪力的测量结果与真实值存在偏差较大
[0025]上述基于惯性力影响的承台结构波浪力试验测量系统,通过在所述承台结构测力模型的顶面、背浪面以及其中一个侧面的中心位置各布置1个单向拉压力传感器和1个位移计,各所述单向拉压力传感器、各所述位移计的一端与所述承台结构测力模型固定连接;所述承台结构测力模型的顶部通过顶面的单向拉压力传感器吊起,顶面的单向拉压力传感器的另一端与顶部的固定支架采用万向球铰接,所述承台结构测力模型的底部与地面无接触,背浪面的单向拉压力传感器与背浪面的固定支架采用万向球铰接,侧面的单向拉压力传感器与该侧面的固定支架采用万向球铰接,顶面的位移计的另一端与顶部的固定支架采用万向球铰接,背浪面的位移计的另一端与背浪面的固定支架采用万向球铰接,该侧面的位移计的另一端与该侧面的固定支架采用万向球铰接,进而采集顶面、背浪面以及侧面的单向拉压力传感器和位移计的变化历时曲线,分析x、y和z方向的单向拉压传感器和位移计对所述承台结构测力模型的作用力以及惯性力,获得所述承台结构测力模型沿x、y和z方向的作用力以及惯性力,再结合力的平衡原理,根据x、y和z方向的单向拉压传感器和位移计对所述承台结构测力模型的作用力以及惯性力进行分析,获得x、y和z方向上所述承台结构测力模型所受的波浪力,从而结合力的合成原理,根据x、y和z方向上所述承台结构测力模型所受的波浪力进行分析,获得所述承台结构测力模型所受的总波浪力。由此,承台结构波浪力试验测量系统将波浪作用下承台结构惯性力部分纳入承台结构波浪力试验测量中,降低结构物所受波浪力的测量结果与真实值的偏差,提高了测量精度。
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Abstract
Description
Technical Field
[0001] This application relates to the field of hydrodynamic measurement technology, and in particular to a wave force test measurement system for a pier structure based on the influence of inertial force. Background Technology
[0002] Due to their large structural dimensions, the abutment section of a cross-sea bridge foundation bears a significant portion of the wave force, making the stress on the abutment a key focus of bridge foundation stress analysis. This stress is typically determined in a laboratory through physical model tests.
[0003] In related technologies, the experimental measurement of wave forces on pier structures generally employs a combination of six-component balances or unidirectional tension / compression sensors. These methods are suitable for measuring the forces acting on structures in equilibrium under constant water flow and wind conditions. However, with wave action, the constantly fluctuating water causes the pier structure's motion response to continuously change, placing it in a non-equilibrium state. Therefore, the pier structure under wave action inevitably experiences a certain amount of inertial force. However, the experimental results obtained using the aforementioned methods do not consider the influence of the structure's own inertial force, leading to significant deviations between the measured wave forces and the actual values. Summary of the Invention
[0004] Therefore, it is necessary to provide a wave force test measurement system for pier structures based on the influence of inertial forces, which can reduce the deviation between the measured results and the true values of wave forces on the structure, in order to address the above-mentioned technical problems.
[0005] A wave force test measurement system for a pier structure based on the influence of inertial force, the system comprising: a uniaxial tension / compression sensor, a displacement gauge, and a force measurement model of the pier structure;
[0006] One uniaxial tension / compression sensor and one displacement meter are arranged at the center of the top surface, the back wave surface, and one of the sides of the bearing structure force measurement model. One end of each uniaxial tension / compression sensor and each displacement meter is fixedly connected to the bearing structure force measurement model.
[0007] The top of the pier structure force measurement model is suspended by a unidirectional tension and compression sensor on the top surface. The other end of the unidirectional tension and compression sensor on the top surface is connected to the top fixed bracket by a universal ball joint. The bottom of the pier structure force measurement model is not in contact with the ground. The other end of the unidirectional tension and compression sensor on the back wave surface is connected to the back wave surface fixed bracket by a universal ball joint. The other end of the unidirectional tension and compression sensor on this side is connected to the side fixed bracket by a universal ball joint.
[0008] The other end of the displacement gauge on the top surface is connected to the fixed bracket on the top surface by a universal ball joint; the other end of the displacement gauge on the back wave surface is connected to the fixed bracket on the back wave surface by a universal ball joint; and the other end of the displacement gauge on this side surface is connected to the fixed bracket on this side surface by a universal ball joint.
[0009] The time-lapse curves of the uniaxial tension and compression sensors and displacement gauges on the top surface, back wave surface, and side surface are collected. The force and inertial force of the uniaxial tension and compression sensors and displacement gauges in the x, y, and z directions on the force measurement model of the pier structure are analyzed to obtain the force and inertial force of the force measurement model of the pier structure in the x, y, and z directions.
[0010] Based on the principle of force balance, the force and inertial force of the pier structure force measurement model are analyzed using unidirectional tension and compression sensors and displacement gauges in the x, y, and z directions to obtain the wave force on the pier structure force measurement model in the x, y, and z directions;
[0011] Based on the principle of force synthesis, the total wave force on the pier structure force measurement model is obtained by analyzing the wave forces acting on the model in the x, y, and z directions.
[0012] In one embodiment, the inertial forces of the pier structure force measurement model along the x, y, and z directions are:
[0013] Inertial force in the x direction:
[0014] Inertial force in the y-direction:
[0015] Inertial force in the z-direction:
[0016] Among them, F mx F my F mz The inertial forces in the x, y, and z directions are respectively, s x (t), s y (t), s z (t) represents the displacement at time t in the x, y, and z directions, respectively. denoted as x, y, and z, respectively, and m is the mass of the force measurement model of the pier structure.
[0017] In one embodiment, the wave forces acting on the pier structure force measurement model in the x, y, and z directions are:
[0018] Wave force in the x-direction:
[0019] Wave force in the y-direction:
[0020] Wave force in the z-direction:
[0021] Among them, F wx (t), F wy (t), F wz (t) represents the wave forces in the x, y, and z directions at time t, respectively, F x (t), F y (t), F z (t) represents the force values of the unidirectional tensile and compressive sensors in the x, y, and z directions at time t.
[0022] In one embodiment, the total wave force on the force measurement model of the pier structure is:
[0023]
[0024] Among them, F w (t) represents the total wave force F acting on the load cell structure model. wx F wy F wz These are the wave forces in the x, y, and z directions, respectively.
[0025] The aforementioned wave force test measurement system for a foundation structure based on the influence of inertial force comprises a uniaxial tension / compression sensor and a displacement gauge positioned at the center of the top surface, the back wave surface, and one of the sides of the foundation structure force measurement model. One end of each uniaxial tension / compression sensor and each displacement gauge is fixedly connected to the foundation structure force measurement model. The top of the foundation structure force measurement model is suspended by the uniaxial tension / compression sensor on the top surface, with the other end of the sensor connected to a fixed support on the top surface via a universal ball joint. The bottom of the foundation structure force measurement model is not in contact with the ground. The uniaxial tension / compression sensor on the back wave surface is connected to a fixed support on the back wave surface via a universal ball joint, as are the uniaxial tension / compression sensors on the sides via a universal ball joint. The other end of the displacement gauge on the top surface is connected to the fixed support on the top surface via a universal ball joint, and the other end of the displacement gauge on the back wave surface is connected to the back wave surface via a universal ball joint. The fixed support adopts a universal ball joint, and the other end of the displacement meter on this side is also connected to the fixed support on this side using a universal ball joint. This allows for the acquisition of the time-lapse curves of the unidirectional tension and compression sensors and displacement meters on the top, back wave, and side surfaces. The forces and inertial forces exerted by the unidirectional tension and compression sensors and displacement meters in the x, y, and z directions on the force measurement model of the pier structure are analyzed to obtain the forces and inertial forces acting on the force measurement model of the pier structure in the x, y, and z directions. Then, combining the principle of force balance, the forces and inertial forces exerted by the unidirectional tension and compression sensors and displacement meters on the force measurement model of the pier structure in the x, y, and z directions are analyzed to obtain the wave forces acting on the force measurement model of the pier structure in the x, y, and z directions. Finally, combining the principle of force composition, the total wave forces acting on the force measurement model of the pier structure in the x, y, and z directions are analyzed to obtain the total wave forces acting on the force measurement model of the pier structure. Therefore, the wave force test and measurement system for pier structures incorporates the inertial force of the pier structure under wave action into the wave force test and measurement of the pier structure, reducing the deviation between the measured wave force of the structure and the true value, and improving the measurement accuracy. Attached Figure Description
[0026] Figure 1 This is a schematic diagram of a wave force testing and measurement system for a pier structure based on the influence of inertial forces, as shown in one embodiment.
[0027] Figure 2 This is a schematic diagram of the data synchronization acquisition structure between a uniaxial tensile / compressive sensor and a displacement gauge in one embodiment.
[0028] Figure 3 This is a schematic diagram of the force duration curve of a unidirectional tensile and compressive sensor in one embodiment;
[0029] Figure 4 This is a schematic diagram of the displacement duration curve of a displacement gauge in one embodiment;
[0030] Figure 5This is a schematic diagram of the force measurement model of the pier structure in one embodiment. Detailed Implementation
[0031] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0032] In one embodiment, such as Figure 1 As shown, a wave force test measurement system for a pier structure based on the influence of inertial force is provided. The system includes: a uniaxial tension and compression sensor, a displacement gauge, and a force measurement model of the pier structure.
[0033] One uniaxial tension / compression sensor and one displacement gauge are arranged at the center of the top surface, the back wave surface, and one of the sides of the force measurement model of the pier structure. One end of each uniaxial tension / compression sensor and each displacement gauge is fixedly connected to the force measurement model of the pier structure. The top of the force measurement model of the pier structure is suspended by the uniaxial tension / compression sensor on the top surface, and the other end of the uniaxial tension / compression sensor on the top surface is connected to the fixed bracket on the top surface by a universal ball joint. The bottom of the force measurement model of the pier structure is not in contact with the ground. The other end of the uniaxial tension / compression sensor on the back wave surface is connected to the fixed bracket on the back wave surface by a universal ball joint, and the other end of the uniaxial tension / compression sensor on the side surface is connected to the fixed bracket on the side surface by a universal ball joint. The other end of the displacement gauge on the top surface is connected to the fixed bracket on the top surface by a universal ball joint, the other end of the displacement gauge on the back wave surface is connected to the fixed bracket on the back wave surface by a universal ball joint, and the other end of the displacement gauge on the side surface is connected to the fixed bracket on the side surface by a universal ball joint.
[0034] The time-lapse curves of uniaxial tension and compression sensors and displacement gauges on the top, back, and side surfaces are collected. The forces and inertial forces exerted by the uniaxial tension and compression sensors and displacement gauges on the bearing structure force measurement model in the x, y, and z directions are analyzed to obtain the forces and inertial forces exerted on the bearing structure force measurement model in the x, y, and z directions. Based on the principle of force balance, the forces and inertial forces exerted by the uniaxial tension and compression sensors and displacement gauges on the bearing structure force measurement model in the x, y, and z directions are analyzed to obtain the wave forces acting on the bearing structure force measurement model in the x, y, and z directions. Based on the principle of force composition, the total wave forces acting on the bearing structure force measurement model in the x, y, and z directions are analyzed to obtain the total wave forces acting on the bearing structure force measurement model.
[0035] Among them, such as Figure 1 As shown, the wave incident direction is the y-direction.
[0036] One uniaxial tension / compression sensor and one displacement gauge are arranged on the top surface of the bearing cap structure force measurement model. One end of the uniaxial tension / compression sensor and the displacement gauge are fixedly connected to the bearing cap structure force measurement model, and the other end is hinged to a fixed support. They primarily measure the force and displacement in the vertical direction (i.e., the z-direction). Similarly, one uniaxial tension / compression sensor and one displacement gauge are arranged on the wave-back surface and one of the side surfaces of the bearing cap structure force measurement model. The wave-back surface is used to measure the horizontal force and displacement along the wave direction (y-direction); the side surface is used to measure the horizontal force and displacement perpendicular to the wave direction (x-direction). The uniaxial tension / compression and displacement must be measured simultaneously.
[0037] Among them, the uniaxial tension and compression sensor can be a uniaxial tension and compression sensor with a sufficient range and capable of recording the force change process in real time.
[0038] Among them, the displacement gauge can be a displacement gauge with a sufficient range and capable of recording the displacement change process in real time.
[0039] The variation time curves can include the force duration curve of the uniaxial tension / compression sensor and the displacement duration curve of the displacement gauge.
[0040] It should be understood that one uniaxial tension / compression sensor and one displacement gauge are arranged at the center of the top surface, the back wave surface, and one of the sides of the bearing platform structure force measurement model to measure the force and displacement in different directions. Compared with the existing six-component balance measurement method, this arrangement can reduce the influence of the deformation of the bearing platform structure force measurement model itself on the force measurement results; compared with the existing uniaxial tension / compression sensor combination measurement method, the number of sensors used in this arrangement method is significantly reduced.
[0041] The weight of the pier structure force measurement model was measured using an electronic scale, and the mass of the pier structure force measurement model was recorded as m, with the unit being kg.
[0042] It should be understood that the universal ball joint between the unidirectional tension / compression sensor, displacement gauge and fixed support can eliminate the influence of the fixed support on the bending moment of the force measurement model of the pier structure.
[0043] In one embodiment, displacement gauges are installed after the unidirectional tensile and compressive sensors are installed. The displacement gauges on the top, back wave, and side surfaces are also connected to the fixed brackets via universal ball joints. This ensures that the displacement gauges are essentially unaffected or subjected to very small forces, meaning that the influence of the displacement gauges on the force measurement model of the pier structure can be ignored.
[0044] Before collecting the time-lapse curves of uniaxial tension / compression sensors and displacement gauges on the top, back, and side surfaces, all uniaxial tension / compression sensors and displacement gauges are first zeroed. To ensure that force and displacement are measured synchronously, a synchronous sampling data acquisition device can be used.
[0045] In one embodiment, the inertial forces along the x, y, and z directions of the force measurement model of the pier structure are:
[0046] Inertial force in the x direction:
[0047] Inertial force in the y-direction:
[0048] Inertial force in the z-direction:
[0049] Among them, F mx F my F mz The inertial forces in the x, y, and z directions are respectively, s x (t), s y (t), s z (t) represents the displacement at time t in the x, y, and z directions, respectively. denoted as x, y, and z, respectively, and m is the mass of the force measurement model of the pier structure.
[0050] in, They are respectively for s x (t), s y (t), s z (t) is obtained by taking the derivative twice.
[0051] In one embodiment, the wave forces acting on the pier structure force measurement model in the x, y, and z directions are:
[0052] Wave force in the x-direction:
[0053] Wave force in the y-direction:
[0054] Wave force in the z-direction:
[0055] Among them, F wx (t), F wy (t), F wz (t) represents the wave forces in the x, y, and z directions at time t, respectively, F x (t), F y (t), F z (t) represents the force values of the unidirectional tensile and compressive sensors in the x, y, and z directions at time t.
[0056] In one embodiment, the total wave force on the force measurement model of the pier structure is:
[0057]
[0058] Among them, Fw (t) represents the total wave force F acting on the load cell structure model. wx F wy F wz These are the wave forces in the x, y, and z directions, respectively.
[0059] The aforementioned wave force test measurement system for a foundation structure based on the influence of inertial force comprises a uniaxial tension / compression sensor and a displacement gauge positioned at the center of the top surface, the back wave surface, and one of the sides of the foundation structure force measurement model. One end of each uniaxial tension / compression sensor and each displacement gauge is fixedly connected to the foundation structure force measurement model. The top of the foundation structure force measurement model is suspended by the uniaxial tension / compression sensor on the top surface, with the other end of the sensor connected to a fixed support on the top surface via a universal ball joint. The bottom of the foundation structure force measurement model is not in contact with the ground. The uniaxial tension / compression sensor on the back wave surface is connected to a fixed support on the back wave surface via a universal ball joint, as are the uniaxial tension / compression sensors on the sides via a universal ball joint. The other end of the displacement gauge on the top surface is connected to the fixed support on the top surface via a universal ball joint, and the other end of the displacement gauge on the back wave surface is connected to the back wave surface via a universal ball joint. The fixed support adopts a universal ball joint, and the other end of the displacement meter on this side is also connected to the fixed support on this side using a universal ball joint. This allows for the acquisition of the time-lapse curves of the unidirectional tension and compression sensors and displacement meters on the top, back wave, and side surfaces. The forces and inertial forces exerted by the unidirectional tension and compression sensors and displacement meters in the x, y, and z directions on the force measurement model of the pier structure are analyzed to obtain the forces and inertial forces acting on the force measurement model of the pier structure in the x, y, and z directions. Then, combining the principle of force balance, the forces and inertial forces exerted by the unidirectional tension and compression sensors and displacement meters on the force measurement model of the pier structure in the x, y, and z directions are analyzed to obtain the wave forces acting on the force measurement model of the pier structure in the x, y, and z directions. Finally, combining the principle of force composition, the total wave forces acting on the force measurement model of the pier structure in the x, y, and z directions are analyzed to obtain the total wave forces acting on the force measurement model of the pier structure. Therefore, the wave force test and measurement system for pier structures incorporates the inertial force of the pier structure under wave action into the wave force test and measurement of the pier structure, reducing the deviation between the measured wave force of the structure and the true value, and improving the measurement accuracy.
[0060] In one embodiment, a schematic diagram of the data synchronization acquisition structure between the uniaxial tension / compression sensor and the displacement gauge is shown below. Figure 2 As shown, the uniaxial tension / compression sensors and displacement gauges in the x, y, and z directions are connected to a synchronous data acquisition unit, which is connected to a computer. The synchronous data acquisition unit simultaneously acquires data from the uniaxial tension / compression sensors and displacement gauges in the x, y, and z directions to generate change duration curves, and transmits the change duration curves to the computer for storage and analysis.
[0061] The schematic diagrams of the force-time curves of the uniaxial tension / compression sensor and the displacement-time curves of the displacement gauge are shown below. Figure 3 and Figure 4 As shown in the figure. In this figure, the unidirectional tensile / compressive sensor has a negative F(t) when compressed and a positive F(t) when under tension. Displacement s is positive along the positive axis and negative along the negative axis.
[0062] The analysis and calculation of wave forces acting on the pier cap structure force measurement model can be based on the classical Newton's second law and the principle of force composition. First, based on the force measurement curves of the unidirectional tension / compression sensors and the change-time curves of the displacement gauges, the forces and inertial forces exerted by the unidirectional tension / compression sensors and displacement gauges on the pier cap structure force measurement model in the x, y, and z directions are obtained. Second, based on the principle of force equilibrium, the wave forces acting on the pier cap structure force measurement model in the x, y, and z directions are calculated. Finally, through the principle of force composition, the total wave force acting on the pier cap structure force measurement model is obtained.
[0063] The force diagram of the pier cap structure force measurement model is as follows: Figure 5 As shown. The specific calculation and analysis process is as follows: First, based on the mass m of the pier structure force measurement model and the displacement duration curve s(t) of the displacement gauge, the inertial forces of the pier structure force measurement model along the x, y, and z directions can be obtained:
[0064] Inertial force in the x direction:
[0065] Inertial force in the y-direction:
[0066] Inertial force in the z-direction:
[0067] In the above formula: F mx F my F mz The inertial forces in the x, y, and z directions are respectively, s x (t), s y (t), s z (t) represents the displacement at time t in the x, y, and z directions, respectively. Indicates s x (t) Find the two derivatives, i.e., the instantaneous acceleration.
[0068] Secondly, considering the force duration curves of the unidirectional tensile and compressive sensors in the x, y, and z directions, and based on the principle of force balance, the wave forces acting on the pier structure force measurement model in the x, y, and z directions are obtained.
[0069] Wave force in the x-direction:
[0070] Wave force in the y-direction:
[0071] Wave force in the z-direction:
[0072] In the formula F wx (t), F wy (t), F wz (t) represent the wave forces in the x, y, and z directions, respectively; F x (t), F y (t), F z (t) represents the force values of the unidirectional tensile and compressive sensors at time t in the x, y, and z directions, respectively.
[0073] Finally, using the principle of force composition, the total wave force F acting on the force measurement model of the pier structure is obtained. w (t)
[0074]
[0075] Compared to existing measurement methods, this application adds an inertial force term F to the force calculation. mx F my F mz .
[0076] The moment of wave forces in each direction on the load cell model can be calculated based on the distance between the measuring point and the bottom of the load cell model.
[0077] The aforementioned wave force test and measurement system for pier structures based on the influence of inertial force incorporates the inertial force of the pier structure under wave action into the wave force test and measurement of the pier structure, thereby reducing the deviation between the measured wave force of the structure and the true value and improving the measurement accuracy.
[0078] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0079] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A wave force testing and measurement system for a pier structure based on the influence of inertial force, characterized in that, The system includes: a uniaxial tension / compression sensor, a displacement meter, and a force measurement model of the pier structure; One uniaxial tension / compression sensor and one displacement meter are arranged at the center of the top surface, the back wave surface, and one of the sides of the bearing structure force measurement model. One end of each uniaxial tension / compression sensor and each displacement meter is fixedly connected to the bearing structure force measurement model. The top of the pier structure force measurement model is suspended by a unidirectional tension and compression sensor on the top surface. The other end of the unidirectional tension and compression sensor on the top surface is connected to the top fixed bracket by a universal ball joint. The bottom of the pier structure force measurement model is not in contact with the ground. The other end of the unidirectional tension and compression sensor on the back wave surface is connected to the back wave surface fixed bracket by a universal ball joint. The other end of the unidirectional tension and compression sensor on this side is connected to the side fixed bracket by a universal ball joint. The other end of the displacement gauge on the top surface is connected to the fixed bracket on the top surface by a universal ball joint; the other end of the displacement gauge on the back wave surface is connected to the fixed bracket on the back wave surface by a universal ball joint; and the other end of the displacement gauge on this side surface is connected to the fixed bracket on this side surface by a universal ball joint. The time-lapse curves of the uniaxial tension and compression sensors and displacement gauges on the top surface, back wave surface, and side surface are collected. The force and inertial force of the uniaxial tension and compression sensors and displacement gauges in the x, y, and z directions on the force measurement model of the pier structure are analyzed to obtain the force and inertial force of the force measurement model of the pier structure in the x, y, and z directions. Based on the principle of force balance, the force and inertial force of the pier structure force measurement model are analyzed using unidirectional tensile and compressive sensors and displacement gauges in the x, y, and z directions to obtain the wave force on the pier structure force measurement model in the x, y, and z directions; Based on the principle of force synthesis, the total wave force on the pier structure force measurement model is obtained by analyzing the wave forces acting on the model in the x, y, and z directions.
2. The system according to claim 1, characterized in that, The inertial forces along the x, y, and z directions of the force measurement model of the pier structure are: Inertial force in the x direction: ; Inertial force in the y-direction: ; Inertial force in the z-direction: ; in, , , These are the inertial forces in the x, y, and z directions, respectively. , , Let be the displacements at time t in the x, y, and z directions, respectively. , , Let be the instantaneous accelerations at time t in the x, y, and z directions, respectively. The mass of the force measurement model of the pier structure is given.
3. The system according to claim 2, characterized in that, The wave forces acting on the pier structure force measurement model in the x, y, and z directions are: Wave force in the x-direction: ; Wave force in the y-direction: ; Wave force in the z-direction: ; in, , , These represent the wave forces in the x, y, and z directions at time t. , , These are the force values of the unidirectional tensile and compressive sensors in the x, y, and z directions at time t.
4. The system according to claim 3, characterized in that, The total wave force on the force measurement model of the pier structure is: ; in, The total wave force on the force measurement model of the pier structure. , , These are the wave forces in the x, y, and z directions, respectively.
Citation Information
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