CN114818191B - Real-time hybrid test method based on shaking table-actuator combined multi-degree-of-freedom loading - Google Patents

Abstract

The invention relates to a real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading, and relates to the technical field of real-time hybrid test. The problem of how to improve the applicability of the real-time hybrid test method and the poor accuracy of restoring force calculation is solved. In the present invention, the test overall structure is firstly divided into a numerical part and a test part, and a model of the corresponding substructure is established, and the seismic wave at the current moment and the restorative force after the correction of the test substructure at the previous moment act together on the upper and lower numerical models respectively. According to the corresponding motion equation, the motion of the upper and lower interfaces of the test substructure is obtained, and according to the motion of the interface, the corresponding control instructions are generated through the sliding mode controller to control the shaking table and the actuator, and at the same time, the motion of the actuator is collected. The sum of the reaction force and the output force of the shaking table is used as the actual restoring force of the test substructure at the current moment, and then the restoring force is corrected, and the above process is repeated as time changes until the seismic wave disappears. Mainly used to calculate resilience.

Description

Real-time hybrid test method based on shaker-actuator combined multi-degree-of-freedom loading

Technical Field

The invention relates to the technical field of real-time mixing test.

Background Art

The real-time hybrid test is one of the most cutting-edge test methods in the current large-scale structural vibration test. Compared with the traditional pseudo-dynamic test, the real-time hybrid test more intuitively and realistically reproduces the response of a part of the overall structure under the real dynamic load. Therefore, under the same model accuracy and boundary reproduction degree, the real-time hybrid test results are often more convincing than the traditional pseudo-dynamic test results. In order to ensure the effectiveness of the loading of the dynamic substructure test, the substructure test carried out with the vibration table as a loading device or part of the loading device is called a vibration table substructure test. Conventional vibration table substructure tests generally divide the upper components of the structure into test substructures, and use the vibration table to simulate the effects of the lower components on them. The advantage is that the test loading equipment is simple.

However, for transverse interlayer shear models such as cable trays, there is no traditional distinction between up and down, but the structure is divided horizontally to the left and right. In this type of test, one side of the test substructure is anchored on the vibration table to load seismic waves, and the other side also requires an actuator to simulate the effect of the numerical substructure on it.

Therefore, the applicability of the real-time hybrid test method in the existing vibration test is poor; and in general tests, the following three problems need to be overcome: 1. How to ensure that the boundary conditions of the structure are accurately reproduced; 2. The coupling loading strategy of the vibration table and the actuator; 3. During the loading process, there is inevitably a time lag between the vibration table and the actuator, which will cause errors in the restoring force transmitted to the numerical substructure. The existing real-time hybrid test method only uses a simplified degree of freedom to conduct the test during the test, which cannot ensure the accurate reproduction of the boundary conditions of the structure, resulting in an increasing cumulative error in the calculation process, coupled with the inevitable time lag, which ultimately leads to poor accuracy in the calculation of the restoring force. In summary, how to improve the applicability and accuracy of the real-time hybrid test method needs to be solved urgently.

Summary of the invention

The purpose of the present invention is to solve the problem of how to improve the applicability of a real-time hybrid test method and the poor accuracy of restoring force calculation. The present invention provides a real-time hybrid test method based on a vibration table-actuator combined with multi-degree-of-freedom loading.

A real-time hybrid test method based on a shaker-actuator combined multi-degree-of-freedom loading method includes:

S1. After the whole test structure is divided into an upper numerical substructure, a test substructure and a lower numerical substructure in sequence along the length direction, the models of the upper numerical substructure, the test substructure and the lower numerical substructure are established, which are the upper numerical model, the test substructure model and the lower numerical model respectively; the test substructure is placed on the vibration table;

S2, when the initial time i=1 is set, the actual restoring force R ₁ of the test substructure is 0, the corrected restoring force R' ₁ of the test substructure is 0, and the elongation of the actuator is 0;

S3. At the i+1th moment, the restoring force _R'1 corrected by the test substructure at the ith moment and the force generated by the seismic wave at the current i+1th moment act together on the motion equations corresponding to the upper and lower numerical models, respectively, to obtain the motion of the upper and lower interfaces, and process the motion of the upper interface through nonlinear transformation to obtain the target elongation of the actuator, while also performing time lag compensation on the actuator; i is an integer, where

The motion of the upper and lower interfaces includes the displacement and rotation angle in the horizontal plane. The upper interface is the interface between the upper numerical substructure and the test substructure, and the lower interface is the interface between the lower numerical substructure and the test substructure.

S4, the sliding mode controller generates a target displacement instruction for driving and controlling the actuator according to the target elongation of the actuator, and also generates a vibration displacement instruction for driving and controlling the vibration table according to the motion of the lower interface. After receiving the instruction, the actuator and the vibration table jointly drive the test substructure to move the test substructure. At this time, the output of the actuator and the vibration table is collected, and the reaction force of the combined force of the actuator and the vibration table output is used as the actual restoring force R _i+1 of the test substructure at the current time i+1;

S5. Correct the restoring force R _i+1 by combining the test substructure model and the actual displacement of the test substructure through a force correction strategy to obtain a corrected restoring force R′ _i+1 ;

S6. Let i=i+1, repeat steps S3 to S5, and gradually integrate and solve until the seismic wave disappears, thus completing the test.

Principle analysis:

The method of the present invention first divides the overall test structure into a numerical part and a test part, and then establishes models of a numerical substructure and a test substructure in a computer. The numerical substructure is calculated in a numerical computer using a step-by-step integration method, and the test substructure is loaded by a vibration table-actuator joint. In the step-by-step integration solution process, the collected restoring force of the test substructure is corrected with the help of a simplified model of the test substructure. In the test loading process, the boundary motion needs to be nonlinearly transformed before it can be transferred to a single actuator for separate loading. At the same time, the collected actuator output also needs to be transformed nonlinearly to obtain the actual restoring force of the test substructure.

Beneficial effects of the present invention:

1. The present invention proposes a real-time hybrid test method based on a shaking table-actuator combined with multi-degree-of-freedom loading, which can be applied to real-time hybrid tests of vertical interlayer structures and transverse interlayer shear model structures, thereby improving the applicability of hybrid tests. A new substructure division method is carried out by adopting a displacement control mode.

Second, the present invention takes into account the coupling between actuators and the nonlinearity of the loading system, thereby avoiding errors caused by the measurement results of the actuators being affected by displacement and rotation angle, making the test results more accurate.

3. The test method described in the present invention adopts a force correction strategy for the measured restoring force after using the conventional time-lag compensation method, which can reduce the accumulated restoring force error in the test and further improve the accuracy of the real-time mixing test.

Fourth, due to the small number of loading devices, conventional hybrid tests often ignore the simulation of other degrees of freedom, resulting in large errors in test results. The present invention can solve this problem well, and accurately simulate the multi-degrees of freedom of the structural boundary by measuring the movement of the interface between the test substructure and the upper and lower numerical substructures, laying a foundation for the accuracy of the test results.

5. The present invention is applicable to the fields of civil engineering, transportation, bridges, aerospace, machinery, and communications engineering, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the principle of the real-time hybrid test method based on the vibration table-actuator combined multi-degree-of-freedom loading according to the present invention;

Fig. 2 is a schematic diagram of the test principle of the substructure division method proposed by the present invention for the three-story building structure model; wherein, _M1 is the mass of the upper numerical substructure, _C1 is the damping of the upper numerical substructure, _K1 is the stiffness of the upper numerical substructure, _M2 is the mass of the upper numerical substructure, _C2 is the damping of the upper numerical substructure, and _K2 is the stiffness of the upper numerical substructure;

FIG3 is a schematic diagram of displacement changes of the test substructure during loading when four actuators and four displacement sensors are arranged;

FIG4 is a schematic diagram of geometric analysis of actuators ChA, ChB, ChC and ChD before and after the test substructure changes; wherein FIG4a is a geometric analysis diagram of actuator ChA before and after the change, FIG4b is a geometric analysis diagram of actuator ChB before and after the change, FIG4c is a geometric analysis diagram of actuator ChC before and after the change, and FIG4d is a geometric analysis diagram of actuator ChD before and after the change.

FIG5 is a schematic diagram of geometric analysis of displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 before and after the test substructure changes; wherein FIG5a is a geometric analysis diagram of displacement sensor LVDT1 before and after the test substructure changes, FIG5b is a geometric analysis diagram of displacement sensor LVDT2 before and after the test substructure changes, FIG5c is a geometric analysis diagram of displacement sensor LVDT3 before and after the test substructure changes, and FIG5d is a geometric analysis diagram of displacement sensor LVDT4 before and after the test substructure changes;

FIG6 is a schematic diagram showing the principle of a novel substructure division method for a continuous beam model proposed by the present invention, wherein FIG6a is a schematic diagram showing the structure of the continuous beam model before division, and FIG6b is a schematic diagram showing the structure of the continuous beam model after division.

In FIG. 3 to FIG. 5 of the above-mentioned drawings, O represents the position of the center of mass of the test substructure in the unloaded state, and G represents the position of the center of mass of the test substructure after loading.

DETAILED DESCRIPTION

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

Referring to FIG. 1 , the present embodiment is described. The real-time hybrid test method based on the vibration table-actuator combined multi-degree-of-freedom loading described in the present embodiment comprises:

S1. After the whole test structure is divided into an upper numerical substructure, a test substructure and a lower numerical substructure in sequence along the length direction, the models of the upper numerical substructure, the test substructure and the lower numerical substructure are established, which are the upper numerical model, the test substructure model and the lower numerical model respectively; the test substructure is placed on the vibration table;

S2, when the initial time i=1 is set, the actual restoring force R ₁ of the test substructure is 0, the corrected restoring force R' ₁ of the test substructure is 0, and the elongation of the actuator is 0;

S3. At the i+1th moment, the restoring force _R'1 corrected by the test substructure at the ith moment and the force generated by the seismic wave at the current i+1th moment act together on the motion equations corresponding to the upper and lower numerical models, respectively, to obtain the motion of the upper and lower interfaces, and process the motion of the upper interface through nonlinear transformation to obtain the target elongation of the actuator, while also performing time lag compensation on the actuator; i is an integer, where

The motion of the upper and lower interfaces includes the displacement and rotation angle in the horizontal plane. The upper interface is the interface between the upper numerical substructure and the test substructure, and the lower interface is the interface between the lower numerical substructure and the test substructure.

S4, the sliding mode controller generates a target displacement instruction for driving and controlling the actuator according to the target elongation of the actuator, and also generates a vibration displacement instruction for driving and controlling the vibration table according to the motion of the lower interface. After receiving the instruction, the actuator and the vibration table jointly drive the test substructure to move the test substructure. At this time, the output of the actuator and the vibration table is collected, and the reaction force of the combined force of the actuator and the vibration table output is used as the actual restoring force R _i+1 of the test substructure at the current time i+1;

S5. Correct the restoring force R _i+1 by combining the test substructure model and the actual displacement of the test substructure through a force correction strategy to obtain a corrected restoring force R _i ′ ₊₁ ;

S6. Let i=i+1, repeat steps S3 to S5, and gradually integrate and solve until the seismic wave disappears, thus completing the test.

In this embodiment, the loading of the test substructure includes the loading of the vibration table and multiple actuators. The loading of the vibration table is the loading of the predetermined earthquake motion record. The loading of the actuator is the result of each actuator obtained by nonlinear change of the numerically calculated target elongation as a command. The actual restoring force Ri ₊₁ includes the restoring force of the actuator and the restoring force of the vibration table. In specific application, the restoring force of the actuator in the actual restoring force Ri ₊₁ can be superimposed with the force generated by the seismic wave and then acted on the motion equation corresponding to the upper numerical model to obtain the motion of the upper interface, and the restoring force of the vibration table in the actual restoring force _Ri+1 can be superimposed with the force generated by the seismic wave and then acted on the motion equation corresponding to the lower numerical model to obtain the motion of the lower interface. The motion equations corresponding to the upper and lower numerical models can be obtained by the existing technology, and the upper and lower numerical models can be determined according to the specific embodiment of the overall structure of the test, and the process of constructing the model in the present invention can be realized by the existing technology.

The preferred test system in this embodiment includes: a numerical calculation system, a signal conversion system, a test loading system and a data acquisition system. Among them, the numerical calculation system mainly includes an electronic computer and a real-time substructure calculation program, and the software is preferably Simulink+Dspace, Labview+NI or other control system related software; the test loading system includes an electro-hydraulic servo actuator, a vibration table system and an MTS controller; the data acquisition system includes a force sensor, a displacement sensor and an acceleration sensor, and the required sensors can be configured separately according to the test requirements.

In this embodiment, the model for establishing the upper numerical substructure, the test substructure and the lower numerical substructure can be obtained by existing technical means, which is specifically determined according to the overall structure of the test;

Furthermore, the actuator specimen system can be approximated by a linear model, expressed as follows:

式中，a₁，a₂，b₁，b₂四个中间变量是由试验识别得到的，四个中间变量分别表示第一至第四项比例系数，d^m和d^c分别为位移命令与响应。

Wherein, _a1 , _a2 , _b1 , _b2 are four intermediate variables obtained by experimental identification, and the four intermediate variables represent the first to fourth proportional coefficients respectively, and ^dm and ^dc are displacement command and response respectively.

The differential equation model of the control object actuator specimen system is as follows:

b ₁ '＝(K _PD +K _N )b ₁ C _F

_b2 '＝( _KPD + _{KN ) b2CF}

_CF ＝( _KN + _KPD + _K'E ) ^-1

为等效力响应，r_E为试验子结构反力，K_PD为拟动力刚度，K_N为数值子结构刚度，K'_E为试验子结构初始切线刚度，C_F为力-位移的转换系数，，b₁'和b'₂均为中间变量。Where u is the input control signal,

is the equivalent force response, r _E is the reaction force of the test substructure, K _PD is the pseudo-dynamic stiffness, K _N is the numerical substructure stiffness, K' _E is the initial tangent stiffness of the test substructure, _CF is the force-displacement conversion coefficient, b ₁ ' and b' ₂ are both intermediate variables.

In this implementation, the middle layer frame is selected as the test substructure, and the upper and lower layers frame are selected as the numerical substructure. This can fully consider the movement of the interface between the test substructure and the upper and lower numerical substructures, and ensure that the boundary conditions of the structure are accurately reproduced. The test substructure uses a three-degree-of-freedom vibration table to simulate the effect of the bottom floor.

Furthermore, in S3, the motion of the upper interface is (dx _i+1 ,dy _i+1 ,θ _i+1 ), and the motion of the lower interface is (dx′ _i+1 ,dy′ _i+1 ,θ′ _i+1 ), where:

dx _i+1 is the displacement of the interface in the x direction in the horizontal plane at the i+1th moment;

dy _i+1 is the displacement of the interface in the y direction in the horizontal plane at the i+1th moment;

θ _i+1 is the rotation angle of the interface at the i+1th moment;

dx′ _i+1 is the displacement of the interface in the x direction in the horizontal plane at the i+1th moment;

dy′ _i+1 is the displacement of the interface in the y direction in the horizontal plane at the i+1th moment;

θ′ _i+1 is the rotation angle of the interface at the i+1th moment.

Furthermore, referring to FIG. 2 and FIG. 3 , the test method is implemented using four actuators, and the settings of the four actuators are highly consistent; wherein,

Actuator ChA and actuator ChB are respectively arranged at positions corresponding to the points dividing the first side of the test substructure into three equal parts in the horizontal direction, and actuator ChC and actuator ChD are respectively arranged at positions corresponding to the points dividing the second side of the test substructure into three equal parts in the horizontal direction, and the sides corresponding to actuator ChA and actuator ChB are adjacent to the sides corresponding to actuator ChC and actuator ChD;

When the test method is implemented using four actuators, the four displacement sensors on the test substructure collect the real displacement components Δl ₁ , Δl ₂ , Δl ₃ and Δl ₄ , thereby obtaining the real displacement of the test substructure;

Among them, Δl ₁ is the true displacement component of the displacement sensor LVDT1 among the four displacement sensors;

Δl ₂ is the true displacement component of displacement sensor LVDT2 among the four displacement sensors;

Δl ₃ is the true displacement component of displacement sensor LVDT3 among the four displacement sensors;

Δl ₄ is the true displacement component of the displacement sensor LVDT4 among the four displacement sensors.

In this preferred embodiment, the test substructure uses a three-degree-of-freedom vibration table to simulate the effect of the bottom floor, and four actuators are used to implement the target command. Actuator ChA and actuator ChB are respectively located at the three-divided points of the first side of the test substructure, and actuator ChC and actuator ChD are respectively located at the three-divided points of the second side of the test substructure. Four displacement sensors are used to measure the actual motion (d _x ″, _dy ″, θ″) of the test substructure.

Loading strategy of actuators: The layout of actuators and displacement sensors and the schematic diagram of structural changes during the loading process are shown in Figure 3. Actuators ChA and ChB are located at the trisection points of the first side of the test substructure, and actuators ChC and ChD are located at the trisection points of the second side of the test substructure. Four displacement sensors are used to measure the true displacements d _x ″ and d _y ″ of the test substructure. The layout of the displacement sensors corresponds to the position of the actuators.

The schematic diagram of the geometric analysis of the actuators ChA, ChB, ChC and ChD before and after the test substructure change is shown in Figure 4. Among them, AD is the length of the actuator after loading.

Furthermore, the four displacement sensors are divided into two groups, wherein displacement sensor LVDT1 and displacement sensor LVDT2 are one group, and displacement sensor LVDT3 and displacement sensor LVDT4 are another group. The two groups of displacement sensors are respectively arranged on the third and fourth side surfaces of the test substructure, and displacement sensor LVDT1 and displacement sensor LVDT2 are respectively arranged opposite to actuator ChA and actuator ChB, and displacement sensor LVDT3 and displacement sensor LVDT4 are respectively arranged opposite to actuator ChC and actuator ChD.

In this preferred embodiment, the arrangement of the displacement sensor corresponds to the position of the actuator. The numerical substructure is calculated in a numerical computer using a step-by-step integration method.

Furthermore, in step S5, the real displacement of the test substructure includes the real displacement d _x ″ of the test substructure relative to the x direction in the ground coordinate system and the real displacement d _y ″ of the test substructure relative to the y direction in the ground coordinate system, and the implementation method of obtaining the real displacement of the test substructure includes:

The expressions of S51, Δl ₁ , Δl ₂ , Δl ₃ and Δl ₄ are:

Wherein, L and S are the length and width of the test substructure respectively; l ₁₀ , l ₂₀ , l ₃₀ and l ₄₀ are the initial lengths of displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 respectively; θ″ is the true inclination angle of the test substructure relative to the ground;

S52. Combine the expressions of Δl ₁ , Δl ₂ , Δl ₃ and Δl ₄ to obtain the values of d _x ″, _dy ″ and θ″.

Furthermore, for any i+1th moment, the expressions for the target elongation Δl _A of the actuator ChA, the target elongation Δl _B of the actuator ChB, the target elongation Δl _C of the actuator ChC, and the target elongation Δl _D of the actuator ChD are:

Wherein, L and S are the length and width of the test substructure respectively; l _A0 , l _B0 , l _C0 and l _D0 are the initial lengths of actuator ChA, actuator ChB, actuator ChC and actuator ChD respectively.

In this preferred embodiment, the geometric analysis diagram of displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 before and after the test substructure changes is shown in Figure 5. Where AD is the length of the displacement meter after loading.

Furthermore, in step S5, the force correction strategy is combined with the test substructure model and the actual displacement of the test substructure to correct the restoring force Ri ₊₁ , and the corrected restoring force _Ri ′ ₊₁ is obtained as follows:

S51, the test substructure model is a linear model, the established test substructure model is Y, and according to the actual displacement difference of the test substructure at two adjacent moments in the model Y of the test substructure and the actual velocity difference of the test substructure at two adjacent moments, the restoring force error ΔR _E,i+1 at the i+1th moment is obtained; the two adjacent moments are the i-th moment and the i+1-th moment respectively;

The velocity difference of the test substructure at two adjacent moments in the model Y of the test substructure is obtained by differentiating the displacement difference of the test substructure at two adjacent moments;

S52. Compensate the actual restoring force R _i+1 using the restoring force error ΔR _E,i+1 to obtain a corrected restoring force R _i ′ ₊₁ .

The motion equations of the two numerical substructures in the force correction state at the i-th moment are:

M _N a _N,i +C _N v _N,i +K _N d _N,i =-M _N a _g -(R _i +ΔR _E,i );

Where M _N is the mass matrix of the numerical substructure;

C _N is the damping matrix of the numerical substructure;

K _N is the stiffness matrix of the numerical substructure;

d _N,i is the displacement vector of the test substructure relative to the ground at the i-th moment;

v _N,i is the velocity vector of the test substructure relative to the ground at the i-th moment;

a _N,i is the acceleration vector of the test substructure relative to the ground at the i-th moment;

a _g is the ground acceleration vector;

R _i is the actual restoring force of the test substructure at the i-th moment;

ΔR _E,i is the restoring force error of the test substructure at the i-th moment.

Furthermore, in step S4, the target displacement command and the vibration displacement command are generated by the sliding mode controller to control the actuator and the vibration table respectively, and the control law w of the sliding mode controller is expressed as:

w=(-(PB ^* ) ^-1 PA ^* -δP ^T B ^* P ^T )Y=k ₁ e _EQ -KZ;

Y＝[e_EQ Z^T]^T；Where, B ^* = [0 B ^T ] ^T ,

Y = [e _EQ Z ^T ] ^T ;

为第四中间变量，e_EQ为实际等效力与等效力命令的误差，Z为控制对象的状态控件模型，k₁是内模增益系数，K为状态反馈增益系数。P is the slip surface coefficient matrix, B ^* is the first intermediate variable matrix, B is the first state space coefficient matrix, A is the second state space coefficient matrix, A ^* is the second intermediate variable matrix, δ is the slip margin, C is the third intermediate variable matrix,

is the fourth intermediate variable, e _EQ is the error between the actual equivalent force and the equivalent force command, Z is the state control model of the controlled object, k ₁ is the internal model gain coefficient, and K is the state feedback gain coefficient.

In this preferred embodiment, in conventional real-time hybrid tests, the hydraulic servo control system generally uses PID control. When the specimen has strong nonlinearity, its control effect will deteriorate or even become unstable. Therefore, the present invention uses a sliding mode controller as an external controller to replace the PID controller to control the actuator and the vibration table. The design of the sliding mode controller is divided into two steps: first, the sliding surface is determined by introducing the concept of internal model control, and then the control law is designed by applying the Lyapulov direct method.

By integrating both sides of the expression of the control law w, the feedback control signal inside the system can be obtained as follows:

Where _k1 is the internal model gain coefficient, _eEQ (τ) is the error function between the actual equivalent force and the equivalent force command, τ is the integral variable, and X(t) is the state quantity of the equivalent force response.

Furthermore, when the structural model is a simple continuous beam model, as shown in Figure 6. The numbers 1 to 6 in Figure 6 all represent the degree of freedom numbers. In Figure 6, the three mass points from left to right are the first to third mass points respectively. Assuming that the model has three concentrated masses and no axial motion, the continuous beam has a total of six degrees of freedom, including the rotation of each mass point and the translation perpendicular to the axis of the beam. In the real-time hybrid test, it can be considered to divide the two mass points on the left into the lower numerical substructure, and the mass point on the right into the test substructure, while the upper numerical substructure does not exist. The lower numerical substructure and the test substructure of the two substructures have 4 and 2 degrees of freedom respectively. If the damping effect is not considered, the kinematic equations of the numerical substructure and the test substructure are:

和

分别为结构模型各个自由度的质量、位移、加速度和地震动加速度记录，i为各个杆件的线刚度，l为相连的两个质量点间连接杆件的长度，I为集中质量点的转动惯量。上式中，m₁为第一个质量点竖向的质量，m₃为第二个质量点竖向的质量，m₅为第三个质量点竖向的质量，x₁为第一个质量点竖向的位移，x₂为第一个质量点的转角，x₃为第二个质量点竖向的位移，x₄为第二个质量点的转角，x₅为第三个质量点竖向的位移x₆为第三个质量点的转角，I₂为第一个质量点的转动惯量，I₄为第二个质量点的转动惯量，I₆为第三个质量点的转动惯量，

为第一个质量点竖向的加速度，

为地震波加速度，

为第一个质量点转角的加速度，

为第二个质量点竖向的加速度，

为第二个质量点转角的加速度，

为第三个质量点竖向的加速度，

为第三个质量点转角的加速度；该刚度矩阵的形式是通过结构力学中受弯杆件的形常数确定的，其计算忽略了杆件截面材料的剪切模量对结构整体刚度的贡献，因此只适用于宽度相比杆件长度可以忽略的杆件体系。运动方程最右边的部分即第二、三个集中质量点的相对位移和转角对恢复力的影响。在新型划分方法中，数值子结构和试验子结构相互传递的不仅仅是剪力，还包括一部分弯矩。In the above formula, _mi , _xi ,

and

are the mass, displacement, acceleration and seismic acceleration records of each degree of freedom of the structural model, i is the linear stiffness of each rod, l is the length of the connecting rod between the two connected mass points, and I is the moment of inertia of the concentrated mass point. In the above formula, _m1 is the vertical mass of the first mass point, _m3 is the vertical mass of the second mass point, _m5 is the vertical mass of the third mass point, _x1 is the vertical displacement of the first mass point, _x2 is the rotation angle of the first mass point, _x3 is the vertical displacement of the second mass point, _x4 is the rotation angle of the second mass point, _x5 is the vertical displacement of the third mass point, _x6 is the rotation angle of the third mass point, _I2 is the moment of inertia of the first mass point, _I4 is the moment of inertia of the second mass point, _I6 is the moment of inertia of the third mass point,

is the vertical acceleration of the first mass point,

is the seismic wave acceleration,

is the acceleration of the first mass point,

is the vertical acceleration of the second mass point,

is the acceleration of the second mass point,

is the vertical acceleration of the third mass point,

is the acceleration of the third mass point rotation; the form of this stiffness matrix is determined by the shape constant of the bending member in structural mechanics. Its calculation ignores the contribution of the shear modulus of the member section material to the overall stiffness of the structure. Therefore, it is only applicable to member systems whose width is negligible compared to the length of the member. The rightmost part of the motion equation is the influence of the relative displacement and rotation of the second and third concentrated mass points on the restoring force. In the new partitioning method, the numerical substructure and the experimental substructure transmit not only shear force but also part of the bending moment.

Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims (9)

1. A real-time hybrid test method based on a vibration table-actuator combined with multi-degree-of-freedom loading, characterized in that the method comprises: S1. After the whole test structure is divided into an upper numerical substructure, a test substructure and a lower numerical substructure in sequence along the length direction, the models of the upper numerical substructure, the test substructure and the lower numerical substructure are established, which are the upper numerical model, the test substructure model and the lower numerical model respectively; the test substructure is placed on the vibration table; S2, when the initial time i=1 is set, the actual restoring force R ₁ of the test substructure is 0, the corrected restoring force R' ₁ of the test substructure is 0, and the elongation of the actuator is 0; S3. At the i+1th moment, the restoring force _R'1 corrected by the test substructure at the ith moment and the force generated by the seismic wave at the current i+1th moment act together on the motion equations corresponding to the upper and lower numerical models, respectively, to obtain the motion of the upper and lower interfaces, and process the motion of the upper interface through nonlinear transformation to obtain the target elongation of the actuator, while also performing time lag compensation on the actuator; i is an integer, where The motion of the upper and lower interfaces includes the displacement and rotation angle in the horizontal plane. The upper interface is the interface between the upper numerical substructure and the experimental substructure, and the lower interface is the interface between the lower numerical substructure and the experimental substructure. S4, the sliding mode controller generates a target displacement command for driving and controlling the actuator according to the target elongation of the actuator, and also generates a vibration displacement command for driving and controlling the vibration table according to the motion of the lower interface. After receiving the command, the actuator and the vibration table jointly drive the test substructure to move the test substructure. At this time, the output of the actuator and the vibration table is collected, and the reaction force of the combined output of the actuator and the vibration table is used as the actual restoring force R _i+1 of the test substructure at the current time i+1; S5. Correct the restoring force R _i+1 by combining the test substructure model and the actual displacement of the test substructure through a force correction strategy to obtain a corrected restoring force R _i ′ ₊₁ ; S6. Let i=i+1, repeat steps S3 to S5, and gradually integrate and solve until the seismic wave disappears, thus completing the test. 2. The real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading according to claim 1 is characterized in that the motion of the upper interface in S3 is (dx _i+1 ,dy _i+1 ,θ _i+1 ), and the motion of the lower interface is (dx _i ′ ₊₁ ,dy _i ′ ₊₁ ,θ _i ′ ₊₁ ), wherein, dx _i+1 is the displacement of the interface in the x direction in the horizontal plane at the i+1th moment; dy _i+1 is the displacement of the interface in the y direction in the horizontal plane at the i+1th moment; θ _i+1 is the rotation angle of the interface at the i+1th moment; dx _i ′ ₊₁ is the displacement of the interface in the x direction in the horizontal plane at the i+1th moment; dy _i ′ ₊₁ is the displacement of the interface in the y direction in the horizontal plane at the i+1th moment; θ _i ′ ₊₁ is the rotation angle of the interface at the i+1th moment. 3. The real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading according to claim 2 is characterized in that the test method is implemented by using four actuators, and the settings of the four actuators are highly consistent; wherein, Actuator ChA and actuator ChB are respectively arranged at positions corresponding to the points dividing the first side of the test substructure into three equal parts in the horizontal direction, and actuator ChC and actuator ChD are respectively arranged at positions corresponding to the points dividing the second side of the test substructure into three equal parts in the horizontal direction, and the sides corresponding to actuator ChA and actuator ChB are adjacent to the sides corresponding to actuator ChC and actuator ChD; When the test method is implemented using four actuators, the four displacement sensors on the test substructure collect the real displacement components Δl ₁ , Δl ₂ , Δl ₃ and Δl ₄ , thereby obtaining the real displacement of the test substructure; Among them, Δl ₁ is the true displacement component of the displacement sensor LVDT1 among the four displacement sensors; Δl ₂ is the true displacement component of displacement sensor LVDT2 among the four displacement sensors; Δl ₃ is the true displacement component of displacement sensor LVDT3 among the four displacement sensors; Δl ₄ is the true displacement component of the displacement sensor LVDT4 among the four displacement sensors. 4. The real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading according to claim 3 is characterized in that the four displacement sensors on the test substructure are arranged at: The four displacement sensors are divided into two groups, wherein displacement sensor LVDT1 and displacement sensor LVDT2 are one group, and displacement sensor LVDT3 and displacement sensor LVDT4 are another group. The two groups of displacement sensors are respectively arranged on the third and fourth sides of the test substructure, and displacement sensor LVDT1 and displacement sensor LVDT2 are respectively arranged opposite to actuator ChA and actuator ChB, and displacement sensor LVDT3 and displacement sensor LVDT4 are respectively arranged opposite to actuator ChC and actuator ChD. 5. The real-time hybrid test method based on shaking table-actuator combined multi-degree-of-freedom loading according to claim 3, characterized in that in step S5, the real displacement of the test substructure includes the real displacement d _x ″ of the test substructure relative to the x direction in the ground coordinate system and the real displacement d _y ″ of the test substructure relative to the y direction in the ground coordinate system, and the implementation method of obtaining the real displacement of the test substructure includes: The expressions of S51, Δl ₁ , Δl ₂ , Δl ₃ and Δl ₄ are:

Wherein, L and S are the length and width of the test substructure respectively; l ₁₀ , l ₂₀ , l ₃₀ and l ₄₀ are the initial lengths of displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 respectively; θ″ is the true inclination angle of the test substructure relative to the ground; S52. Combine the expressions of Δl ₁ , Δl ₂ , Δl ₃ and Δl ₄ to obtain the values of d _x ″, _dy ″ and θ″. 6. The real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading according to claim 3, characterized in that, for any i+1th moment, the expressions of the target elongation Δl _A of the actuator ChA, the target elongation Δl _B of the actuator ChB, the target elongation Δl _C of the actuator ChC and the target elongation Δl _D of the actuator ChD are:

Wherein, L and S are the length and width of the test substructure respectively; l _A0 , l _B0 , l _C0 and l _D0 are the initial lengths of actuator ChA, actuator ChB, actuator ChC and actuator ChD respectively. 7. The real-time hybrid test method based on the shaking table-actuator combined multi-degree-of-freedom loading according to claim 1, characterized in that in step S5, the restoring force Ri ₊₁ is corrected by combining the test substructure model and the actual displacement of the test substructure through a force correction strategy, and the implementation method of obtaining the corrected restoring force _Ri ′ ₊ 1 is as follows: S51, the test substructure model is a linear model, the established test substructure model is Y, and according to the actual displacement difference of the test substructure at two adjacent moments in the model Y of the test substructure and the actual velocity difference of the test substructure at two adjacent moments, the restoring force error ΔR _E,i+1 at the i+1th moment is obtained; the two adjacent moments are the i-th moment and the i+1-th moment respectively; The velocity difference of the test substructure at two adjacent moments in the model Y of the test substructure is obtained by differentiating the displacement difference of the test substructure at two adjacent moments; S52. Compensate the actual restoring force R _i+1 using the restoring force error ΔR _E,i+1 to obtain a corrected restoring force R _i ′ ₊₁ . 8. The real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading according to claim 1 is characterized in that the motion equations of the two numerical substructures in the force correction state at the i-th moment are: M _N a _N,i +C _N v _N,i +K _N d _N,i =-M _N a _g -(R _i +ΔR _E,i ); Where M _N is the mass matrix of the numerical substructure; C _N is the damping matrix of the numerical substructure; K _N is the stiffness matrix of the numerical substructure; d _N,i is the displacement vector of the test substructure relative to the ground at the i-th moment; v _N,i is the velocity vector of the test substructure relative to the ground at the i-th moment; a _N,i is the acceleration vector of the test substructure relative to the ground at the i-th moment; a _g is the ground acceleration vector; R _i is the actual restoring force of the test substructure at the i-th moment; ΔR _E,i is the restoring force error of the test substructure at the i-th moment. 9. The real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading according to claim 1 is characterized in that, in step S4, the expression of the control law w of the sliding mode controller is:

in,

C = [01]; P is the slip surface coefficient matrix, B ^* is the first intermediate variable matrix, B is the first state space coefficient matrix, A is the second state space coefficient matrix, A ^* is the second intermediate variable matrix, δ is the slip margin, C is the third intermediate variable matrix,

is the fourth intermediate variable, e _EQ is the error between the actual equivalent force and the equivalent force command, Z is the state control model of the controlled object, k ₁ is the internal model gain coefficient, and K is the state feedback gain coefficient.

Images