CN114818191B - Real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading - Google Patents
Real-time hybrid test method based on vibration table-actuator combined multi-degree-of-freedom loading Download PDFInfo
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Abstract
A real-time mixing test method based on a vibration table-actuator combined multi-degree-of-freedom loading relates to the technical field of real-time mixing tests. The problem of how to promote the applicability and the poor restoring force calculation accuracy of the real-time hybrid test method is solved. The invention firstly divides the whole test structure into a numerical value part and a test part, establishes models of corresponding substructures, obtains the motion amount of the upper and lower interfaces of the test substructure by the combined action of the seismic waves at the current moment and the restoring force of the test substructure corrected at the previous moment on the motion equations respectively corresponding to the upper and lower numerical value models, generates corresponding control instructions to control the vibration table and the actuator through a sliding mode controller according to the motion amount of the interfaces, collects the sum of the counter forces of the actuator and the vibration table, takes the sum as the actual restoring force of the test substructure at the current moment, corrects the restoring force, and continuously repeats the process along with the time change until the seismic waves disappear. Mainly for calculating the restoring force.
Description
Technical Field
The invention relates to the technical field of real-time mixing tests.
Background
The real-time mixing test is one of the leading test methods in the vibration test of the current large-scale structure. Compared with the traditional simulated dynamic force test, the real-time hybrid test more intuitively and truly reproduces the response of a part of the whole structure under the real dynamic load, so that the real-time hybrid test result is more convincing than the traditional simulated dynamic force test result under the condition that the model precision and the boundary reproduction degree are the same. In order to ensure the effectiveness of loading on the dynamic substructure test, the vibration table is taken as a loading device or a part of the loading device, and the developed substructure test is called a vibration table substructure test. Conventional vibrating table substructure tests typically divide the structural upper member into test substructures, which are simulated by the vibrating table, with the advantage that the test loading equipment is simple.
However, for a transverse interlaminar shear model similar to a cabling rack, the structure is divided horizontally upwards, left and right, without division in the traditional sense, in such tests, one side of a test substructure is anchored on a 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 real-time mixing test method in the existing vibration test has poor applicability; in general, three problems need to be overcome: 1. how to ensure that the boundary condition of the structure is accurately reproduced; 2. a coupling loading strategy of the vibration table and the actuator; 3. during loading, the vibration table and the actuator are inevitably subjected to a time lag, which makes the restoring force transmitted to the numerical substructure erroneous. The existing real-time hybrid test method only utilizes one simplified degree of freedom to test in the test process, and cannot ensure that the boundary condition of the structure is accurately reproduced, so that the accumulated error in the calculation process is continuously increased, and the inevitable time lag finally causes poor calculation accuracy of restoring force.
Disclosure of Invention
The invention aims to solve the problem that how to improve the applicability and poor computational accuracy of restoring force of a real-time mixing test method, and provides a vibration table-actuator combined multi-degree-of-freedom loading real-time mixing test method.
A real-time hybrid test method based on a vibration table-actuator combined multi-degree-of-freedom loading comprises the following steps:
s1, after a test overall structure is sequentially divided into an upper numerical value substructure, a test substructure and a lower numerical value substructure along the length direction, models of the upper numerical value substructure, the test substructure and the lower numerical value substructure are established, wherein the models are an upper numerical value model, a test substructure model and a lower numerical value model respectively; the test substructure is placed on a vibration table;
s2, testing the actual restoring force of the substructure when the initial time i =1R 1 =0, post-correction restoring force R 'of test substructure' 1 =0, actuator elongation is 0;
s3, at the (i + 1) th time, correcting the restoring force R 'of the test substructure at the time i' 1 The force generated by the seismic waves at the current (i + 1) th moment and the force generated by the seismic waves act on motion equations respectively corresponding to the upper and lower numerical models to obtain the motion amount of an upper interface and a lower interface, the motion amount of the upper interface is processed through nonlinear transformation to obtain the target elongation of the actuator, and meanwhile, time lag compensation is carried out on the actuator; i is an integer in which, among others,
the movement amount of the upper interface and the movement amount of the lower interface both comprise displacement and rotation angles in a horizontal plane, the upper interface is an interface between the upper numerical value substructure and the test substructure, and the lower interface is an interface between the lower numerical value substructure and the test substructure;
s4, slip mode controller generates the target displacement instruction that carries out drive control to the actuator according to the target elongation of actuator, still generate the vibrations displacement instruction that carries out drive control to the shaking table according to the amount of exercise of interface down, actuator and shaking table receive the instruction after, drive the test substructure jointly and make the test substructure produce and remove, at this moment, gather the power of exerting oneself of actuator and shaking table, and exert the counter-force of resultant force with actuator and shaking table, as the actual restoring force R of the test substructure at present i +1 moment i+1 ；
S5, correcting the restoring force R by combining a force correction strategy with the test substructure model and the real displacement of the test substructure i+1 Obtaining a corrected restoring force R' i+1 ；
And S6, enabling i = i +1, repeatedly executing the steps from S3 to S5, gradually integrating and solving until the seismic waves disappear, and finishing the test.
Principle analysis:
the method comprises the steps of dividing a test overall structure into a numerical value part and a test part, establishing models of a numerical value substructure and the test substructure in a computer, calculating the numerical value substructure in the numerical value computer by adopting a step-by-step integration method, and loading the test substructure by adopting a vibration table-actuator combination. And in the solving process of the gradual integral, correcting the acquired restoring force of the test substructure by using a simplified model of the test substructure. In the test loading process, the boundary motion amount needs to be subjected to nonlinear transformation to be transmitted to a single actuator to be independently loaded, and meanwhile, the collected actuator output force also needs to be subjected to nonlinear transformation to obtain the actual restoring force of the test substructure.
The invention has the beneficial effects that:
1. the invention provides a real-time mixing test method based on a vibration table-actuator combined multi-degree-of-freedom loading, which can be applied to a real-time mixing test of a vertical interlayer structure and a transverse interlayer shearing model structure as a whole, and improves the applicability of the mixing test. And a displacement control mode is adopted, and a novel substructure dividing mode is carried out.
2. According to the invention, the coupling between the actuators and the nonlinearity of the loading system are considered, so that errors caused by the influence of displacement and rotation angle on the measurement result of the actuators are avoided, and the test result is more accurate.
3. According to the test method, after a conventional time-lag compensation method is used, a force correction strategy is adopted for the measured restoring force, so that the restoring force error accumulated in the test can be reduced, and the accuracy of the real-time mixing test is further improved.
4. Conventional mixing tests often neglect simulation of other degrees of freedom due to less loading equipment, resulting in larger error of test results. The invention can well solve the problems, accurately simulate the multiple degrees of freedom of the structure boundary by the motion amount of the interface between the test substructure and the upper and lower numerical substructure, and lay a foundation for the accuracy of the test result.
5. The invention is suitable for the fields of civil engineering, traffic, bridges, aerospace, machinery, communication engineering and the like.
Drawings
FIG. 1 is a schematic diagram of a real-time hybrid test method based on a combination of a vibration table and an actuator and multi-degree of freedom loading according to the present invention;
FIG. 2 shows the present inventionA schematic diagram of a test principle under a substructure division mode is provided for a three-layer building structure model; wherein M is 1 Is the mass of the upper numerical substructure, C 1 Damping of upper numerical substructures, K 1 Is the stiffness of the upper numerical substructure, M 2 Is the mass of the upper numerical substructure, C 2 Damping of upper numerical substructures, K 2 Is the stiffness of the upper numerical substructure;
FIG. 3 is a schematic diagram of the displacement change of the test substructure during the loading process under 4 actuators and 4 displacement sensor arrangements;
FIG. 4 is a schematic diagram of the geometric analysis of actuators ChA, chB, chC and ChD before and after a change in the substructures of the assay; wherein FIG. 4a is a geometric analysis diagram of the actuator ChA before and after the change, FIG. 4b is a geometric analysis diagram of the actuator ChB before and after the change, FIG. 4c is a geometric analysis diagram of the actuator ChC before and after the change, FIG. 4d is a geometric analysis diagram of the actuator ChD before and after the change,
FIG. 5 is a schematic diagram of the geometric analysis of the displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 before and after the change of the test substructure; fig. 5a is a geometric analysis diagram of the displacement sensor LVDT1 before and after the test substructure is changed, fig. 5b is a geometric analysis diagram of the displacement sensor LVDT2 before and after the test substructure is changed, fig. 5c is a geometric analysis diagram of the displacement sensor LVDT3 before and after the test substructure is changed, and fig. 5d is a geometric analysis diagram of the displacement sensor LVDT4 before and after the test substructure is changed;
fig. 6 is a schematic diagram of a principle of a novel substructure division manner proposed for a continuous beam model in the present invention, where fig. 6a is a schematic diagram of a structure of the continuous beam model before being divided, and fig. 6b is a schematic diagram of a structure of the continuous beam model after being divided.
In fig. 3 to 5 of the above drawings, O denotes the position of the centroid of the test substructure in the unloaded state, and G denotes the position of the centroid of the test substructure after loading.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive efforts based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
Referring to fig. 1, the embodiment is described, and the method for the real-time hybrid test based on the combination of the vibration table and the actuator with multiple degrees of freedom loading in the embodiment comprises the following steps:
s1, after a test overall structure is sequentially divided into an upper numerical substructure, a test substructure and a lower numerical substructure along the length direction, models of the upper numerical substructure, the test substructure and the lower numerical substructure are established and are respectively an upper numerical model, a test substructure model and a lower numerical model; the test substructure is placed on a vibration table;
s2, when the initial time i =1 is set, testing the actual restoring force R of the substructure 1 =0, post-correction restoring force R 'of test substructure' 1 =0, actuator elongation is 0;
s3, at the (i + 1) th time, the restoring force R 'after the test substructure at the time i is corrected' 1 The force generated by the seismic waves at the current (i + 1) th moment and the force generated by the seismic waves act on motion equations respectively corresponding to the upper and lower numerical models to obtain the motion amount of an upper interface and a lower interface, the motion amount of the upper interface is processed through nonlinear transformation to obtain the target elongation of the actuator, and meanwhile, time lag compensation is carried out on the actuator; i is an integer in which, in the formula,
the movement amount of the upper interface and the movement amount of the lower interface both comprise displacement and rotation angles in a horizontal plane, the upper interface is an interface between the upper numerical value substructure and the test substructure, and the lower interface is an interface between the lower numerical value 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 movement amount of the lower interface to doAfter the actuator and the vibration table receive the instruction, the test substructure is driven together to move, at the moment, the output force of the actuator and the vibration table is collected, and the counter force of the resultant force of the output force of the actuator and the vibration table is used as the actual restoring force R of the test substructure at the current i +1 moment i+1 ；
S5, correcting the restoring force R by combining a force correction strategy with the test substructure model and the real displacement of the test substructure i+1 Obtaining a corrected restoring force R i ′ +1 ；
And S6, enabling i = i +1, repeatedly executing the steps S3 to S5, gradually integrating and solving until the seismic waves disappear, and finishing the test.
In this embodiment, the loading of the test substructure includes the loading of shaking table and a plurality of actuators, and the loading of shaking table is the loading of setting earthquake motion record, and the loading of actuator is the result of each actuator that target elongation that numerical value calculated obtained through nonlinear change is as the command, and actual restoring force R i+1 The restoring force of the actuator and the restoring force of the vibration table are included, and the actual restoring force R can be used in specific application i+1 The restoring force of the actuator in the system and the force generated by the seismic wave are superposed and jointly acted on a motion equation corresponding to the upper numerical model to obtain the motion amount of an upper intersection surface and the actual restoring force R i+1 After the restoring force of the vibration table and the force generated by seismic waves are superposed, the restoring force and the force are acted on a motion equation corresponding to a lower numerical model together to obtain the motion amount of a lower interface, wherein the motion equations respectively corresponding to the upper numerical model and the lower numerical model can be obtained through the prior art, the upper numerical model and the lower numerical model can be determined according to the concrete embodiment form of the whole test structure, and the process of constructing the models in the invention can be realized through the prior art.
The preferred test system in this embodiment comprises: the device comprises a numerical calculation system, a signal conversion system, a test loading system and a data acquisition system. The numerical calculation system mainly comprises 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 comprises an electro-hydraulic servo actuator, a vibration table system and an MTS controller; the data acquisition system comprises a force sensor, a displacement sensor and an acceleration sensor, and the required sensors can be additionally configured according to test requirements.
In this embodiment, the models for establishing the upper numerical substructure, the test substructure and the lower numerical substructure may be obtained by means of the prior art, which is specifically determined according to the test overall structure;
further, the actuator test piece system can be approximated by a linear model, as follows:
The differential equation model of the control object actuator test piece system is as follows:
b 1 '＝(K PD +K N )b 1 C F
b 2 '＝(K PD +K N )b 2 C F
C F ＝(K N +K PD +K' E ) -1
wherein u is an input control signal,
in response to an equivalent effect, r E To test substructure reaction, K PD To simulate dynamic stiffness, K N Is numerical substructure stiffness, K' E To test the initial tangential stiffness of the substructure, C F Is the force-displacement conversion coefficient, b 1 'and b' 2 Are all intermediate variables.
In the embodiment, the middle layer of frame is selected as the test substructure, and the upper and lower layers of frames are selected as the numerical substructures, so that the motion amount of the interfaces between the test substructure and the upper and lower numerical substructures respectively can be fully considered, and the boundary conditions of the structure can be ensured to be accurately reproduced. The test substructure adopts a three-degree-of-freedom vibration table to simulate the effect of a bottom floor.
Furthermore, the movement amount of the middle and upper interface in S3 is (dx) i+1 ,dy i+1 ,θ i+1 ) The moving amount of the lower interface is (dx' i+1 ,dy′ i+1 ,θ′ i+1 ) Wherein
dx i+1 the displacement of the interface in the x direction in the horizontal plane at the (i + 1) th moment;
dy i+1 the displacement of the interface in the y direction in the horizontal plane at the (i + 1) th moment;
θ i+1 the corner of the interface at the (i + 1) th moment;
dx′ i+1 the displacement of the lower interface in the x direction in the horizontal plane at the (i + 1) th moment;
dy′ i+1 the displacement of the lower interface in the y direction in the horizontal plane at the time point i + 1;
θ′ i+1 the angle of rotation of the lower interface at time i + 1.
Further, referring specifically to fig. 2 and 3, the test method is implemented by using 4 actuators, and the setting heights of the 4 actuators are consistent; wherein,
the actuator ChA and the actuator ChB are respectively arranged at the corresponding positions of the trisection points of the first side surface of the test substructure in the horizontal direction, the actuator ChC and the actuator ChD are respectively arranged at the corresponding positions of the trisection points of the second side surface of the test substructure in the horizontal direction, and the corresponding side surfaces of the actuator ChA and the actuator ChB are adjacent to the corresponding side surfaces of the actuator ChC and the actuator ChD;
when the test method is realized by adopting 4 actuators, the real displacement component delta l is correspondingly acquired by 4 displacement sensors on the test substructure 1 、Δl 2 、Δl 3 And Δ l 4 Thereby to makeObtaining the real displacement of the test substructure;
wherein,. DELTA.l 1 The real displacement component of the displacement sensor LVDT1 in the 4 displacement sensors;
Δl 2 the real displacement component of the displacement sensor LVDT2 in the 4 displacement sensors;
Δl 3 is the real displacement component of the displacement sensor LVDT3 in the 4 displacement sensors;
Δl 4 is the real displacement component of the displacement sensor LVDT4 of the 4 displacement sensors.
In the preferred embodiment, the test substructure adopts a three-degree-of-freedom vibration table to simulate the bottom floor, four actuators are adopted to realize the target command, the actuator ChA and the actuator ChB are respectively arranged at trisection points of the first side surface of the test substructure, and the actuator ChC and the actuator ChD are respectively arranged at trisection points of the second side surface of the test substructure. Four displacement sensors are used to measure the actual amount of motion (d) of the test substructure x ″,d y ″,θ″)。
Loading strategy of the actuator: a schematic diagram of the actuator and displacement sensor arrangement and structural changes to the loading process is shown in fig. 3. The actuator ChA and the actuator ChB are respectively arranged at trisection points of the first side surface of the test substructure, the actuator ChC and the actuator ChD are respectively arranged at trisection points of the second side surface of the test substructure, and 4 displacement sensors are adopted to measure the real displacement d of the test substructure x "and d y The placement of the displacement sensor corresponds to the position of the actuator.
A schematic of the geometric analysis of actuators ChA, chB, chC and ChD before and after the change in the substructures is shown in FIG. 4. Where AD is the loaded actuator length.
Furthermore, the 4 displacement sensors are divided into two groups, wherein the displacement sensor LVDT1 and the displacement sensor LVDT2 are taken as one group, the displacement sensor LVDT3 and the displacement sensor LVDT4 are taken as the other group, the two groups of displacement sensors are respectively arranged on the third fourth side surface of the test substructure, the displacement sensor LVDT1 and the displacement sensor LVDT2 are respectively arranged opposite to the actuator ChA and the actuator ChB, and the displacement sensor LVDT3 and the displacement sensor LVDT4 are respectively arranged opposite to the actuator ChC and the actuator ChD.
In the preferred embodiment, the displacement sensor is arranged to correspond to the position of the actuator. The numerical substructure is calculated in a numerical computer using a stepwise integration method.
Furthermore, the real displacement of the test substructure in step S5 includes the real displacement d of the test substructure relative to the x-direction in the ground coordinate system x "and the true displacement d of the test substructure relative to the y-direction in the ground coordinate system y And the implementation of obtaining the true displacement of the test substructure includes:
S51、Δl 1 、Δl 2 、Δl 3 and Δ l 4 The expressions are respectively:
wherein, L and S are respectively the length and the width of the test substructure; l. the 10 、l 20 、l 30 And l 40 The initial lengths of the displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 are respectively, and theta' is the real inclination angle of the test substructure relative to the ground;
s52, converting delta l 1 、Δl 2 、Δl 3 And Δ l 4 Expression simultaneous, obtaining d x ″、d y "and θ".
Further, for any time instant i +1,target elongation Δ l of actuator ChA A Target elongation Δ l of actuator ChB B Target elongation Deltal of actuator ChC C And target elongation Δ l of actuator ChD D The expression of (c) is:
wherein, L and S are respectively the length and the width of the test substructure; l. the A0 、l B0 、l C0 And l D0 The initial lengths of actuator ChA, actuator ChB, actuator ChC and actuator ChD are shown.
In the preferred embodiment, a schematic diagram of the geometric analysis of the displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 before and after the test substructure is changed is shown in fig. 5. Where AD is the length of the displacement gauge after loading.
Further, in step S5, the restoring force R is corrected by a force correction strategy in combination with the model of the test substructure and the actual displacement of the test substructure i+1 Obtaining a corrected restoring force R i ′ +1 The implementation mode of the method is as follows:
s51, the test substructure model is a linear model, the established test substructure model is Y, and the restoring force error delta R at the (i + 1) th moment is obtained according to the actual displacement difference of the test substructure at two adjacent moments and the actual speed difference of the test substructure at the two adjacent moments in the test substructure model Y E,i+1 (ii) a Two adjacent to each otherThe time is the ith time and the (i + 1) th time respectively;
the speed 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, utilizing restoring force error delta R E,i+1 To actual restoring force R i+1 Compensating to obtain a corrected restoring force R i ′ +1 。
The motion equations of the two numerical substructures in the force correction state at the ith moment are both as follows:
M N a N,i +C N v N,i +K N d N,i ＝-M N a g -(R i +ΔR E,i )；
wherein M is N A quality matrix being a numerical substructure;
C N a damping matrix being a numerical substructure;
K N a stiffness matrix being a numerical substructure;
d N,i a displacement vector of the test substructure relative to the ground at the ith moment;
v N,i testing the velocity vector of the substructure relative to the ground at the ith moment;
a N,i testing the acceleration vector of the substructure relative to the ground at the ith moment;
a g the earthquake dynamic acceleration vector is obtained;
R i testing the actual restoring force of the substructure for the ith time;
ΔR E,i the restoring force error of the substructure is tested for time i.
Further, 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 expression of the control law w of the sliding mode controller is:
w＝(-(PB * ) -1 PA * -δP T B * P T )Y＝k 1 e EQ -KZ；
wherein, B * ＝[0 B T ] T ，
Y＝[e EQ Z T ] T ；
P is a slip plane coefficient matrix, B * Is a first intermediate variable matrix, B is a first state space coefficient matrix, A is a second state space coefficient matrix, A * Is a second intermediate variable matrix, delta is a slip margin, C is a third intermediate variable matrix,
is a fourth intermediate variable, e EQ Error of actual equivalence power and equivalence power command, Z is state control model of control object, k 1 Is the internal model gain coefficient, and K is the state feedback gain coefficient.
In the preferred embodiment, in a conventional real-time mixing test, the hydraulic servo control system generally adopts PID control, and when a test piece has strong nonlinearity, the control effect will be poor or even unstable, so that the sliding mode controller is adopted as an external controller to replace the PID controller to control the actuator and the vibration table. The sliding mode controller design is divided into two steps: firstly, determining a slip plane by introducing an internal model control concept, and then designing a control law by applying a Lyapunov direct method.
The feedback control signal inside the system obtained by integrating the expression of the control law w at two sides is as follows:
in the formula, k 1 Is the gain coefficient of the internal model, e EQ (τ) is the error function of the actual isopower and the isopower command, τ is the integral variable, and X (t) is the state quantity of the isopower response.
Further, when the structural form is a simple continuous beam form, as shown in FIG. 6. Numbers 1 to 6 in fig. 6 all represent the number of degrees of freedom, and in fig. 6, three mass points from left to right are respectively the first to third mass points, and assuming that the model has three concentrated masses and no axial motion, the continuous beam has six degrees of freedom in total, including rotation of each mass point and translation perpendicular to the axial direction of the beam. In the real-time hybrid test, the left two quality points can be divided into a lower numerical substructure, the right one quality point can be divided into a test substructure, the upper numerical substructure does not exist, and 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 experimental substructure are respectively as follows:
in the above formula, m i 、x i 、
And &>
And recording the mass, displacement, acceleration and seismic acceleration of each degree of freedom of the structural model respectively, wherein I is the linear stiffness of each rod piece, l is the length of a connecting rod piece between two connected mass points, and I is the rotational inertia of a concentrated mass point. In the above formula, m 1 Mass vertical to the first mass point, m 3 Mass in the vertical direction of the second mass point, m 5 Mass vertical to the third mass point, x 1 Is the vertical displacement of the first mass point, x 2 Angle of rotation, x, of the first mass point 3 Is the vertical displacement of the second mass point, x 4 Angle of rotation, x, of the second mass point 5 Is a vertical displacement x of the third mass point 6 Is the angle of rotation of the third mass point, I 2 As rotation of the first mass pointInertia, I 4 Moment of inertia of the second mass point, I 6 Is the moment of inertia of the third mass point, <' > is greater than or equal to>
For the acceleration in the vertical direction of the first mass point, is greater than>
For seismic acceleration, based on>
Acceleration for a first mass point angle>
Acceleration in the vertical direction for the second mass point, based on the measured value>
Acceleration of the second mass point angle->
Acceleration in the vertical direction for the third mass point>
Acceleration at a third mass point corner; the form of the rigidity matrix is determined by the shape constant of the flexural bar in structural mechanics, and the calculation ignores the contribution of the shear modulus of the cross-section material of the bar to the overall rigidity of the structure, so that the rigidity matrix is only suitable for bar systems with the width being negligible compared with the length of the bar. The influence of the relative displacements and rotation angles of the rightmost part of the equation of motion, i.e., the second and third concentrated mass points, on the restoring force. In the novel partitioning method, the numerical substructure and the test substructure transmit to each other not only shear forces but also a part of the bending moment.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative 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 features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.
Claims (9)
1. The real-time mixed test method based on the combination of the vibration table and the actuator and the multi-degree-of-freedom loading is characterized by comprising the following steps of:
s1, after a test overall structure is sequentially divided into an upper numerical substructure, a test substructure and a lower numerical substructure along the length direction, models of the upper numerical substructure, the test substructure and the lower numerical substructure are established and are respectively an upper numerical model, a test substructure model and a lower numerical model; the test substructure is placed on a vibration table;
s2, when the initial time i =1 is set, testing the actual restoring force R of the substructure 1 =0, post-correction restoring force R 'of test substructure' 1 =0, actuator elongation is 0;
s3, at the (i + 1) th time, the restoring force R 'after the test substructure at the time i is corrected' 1 The force generated by the seismic waves at the current (i + 1) th moment and the force generated by the seismic waves act on motion equations respectively corresponding to the upper and lower numerical models to obtain the motion amount of an upper interface and a lower interface, the motion amount of the upper interface is processed through nonlinear transformation to obtain the target elongation of the actuator, and meanwhile, time lag compensation is carried out on the actuator; i is an integer in which, in the formula,
the movement amount of the upper interface and the movement amount of the lower interface both comprise displacement and rotation angles in a horizontal plane, the upper interface is an interface between the upper numerical value substructure and the test substructure, and the lower interface is an interface between the lower numerical value 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 motion amount of a lower interface according to the motion amount of the lower interfaceThe vibration displacement instruction for driving and controlling the vibration table is generated, the actuator and the vibration table drive the test substructure jointly to enable the test substructure to move after receiving the instruction, at the moment, the output force of the actuator and the vibration table is collected, and the counter force of the output resultant force of the actuator and the vibration table is used as the actual restoring force R of the test substructure at the current i +1 moment i+1 ；
S5, correcting the restoring force R by combining a force correction strategy with the test substructure model and the real displacement of the test substructure i+1 Obtaining a corrected restoring force R i ′ +1 ；
And S6, enabling i = i +1, repeatedly executing the steps S3 to S5, gradually integrating and solving until the seismic waves disappear, and finishing the test.
2. The real-time hybrid test method based on the combination of the vibration table and the actuator and the multi-degree of freedom loading as claimed in claim 1, wherein the amount of motion of the middle and upper interface of S3 is (dx) i+1 ,dy i+1 ,θ i+1 ) The amount of movement of the lower interface is (dx) i ′ +1 ,dy i ′ +1 ,θ i ′ +1 ) Wherein
dx i+1 the displacement of the interface in the x direction in the horizontal plane at the (i + 1) th moment;
dy i+1 the displacement of the interface in the y direction in the horizontal plane at the (i + 1) th moment;
θ i+1 the corner of the interface at the (i + 1) th moment;
dx i ′ +1 the displacement of the lower interface in the x direction in the horizontal plane at the moment i + 1;
dy i ′ +1 the displacement of the lower interface in the y direction in the horizontal plane at the moment i + 1;
θ i ′ +1 the angle of rotation of the lower interface at time i + 1.
3. The real-time hybrid test method based on the combination of the vibration table and the actuator and the multi-degree-of-freedom loading as claimed in claim 2 is characterized in that the test method is realized by adopting 4 actuators, and the setting heights of the 4 actuators are consistent; wherein,
the actuator ChA and the actuator ChB are respectively arranged at the corresponding positions of the trisection points of the first side surface of the test substructure in the horizontal direction, the actuator ChC and the actuator ChD are respectively arranged at the corresponding positions of the trisection points of the second side surface of the test substructure in the horizontal direction, and the corresponding side surfaces of the actuator ChA and the actuator ChB are adjacent to the corresponding side surfaces of the actuator ChC and the actuator ChD;
when the test method is realized by adopting 4 actuators, the real displacement component delta l is correspondingly acquired by 4 displacement sensors on the test substructure 1 、Δl 2 、Δl 3 And Δ l 4 So as to obtain the real displacement of the test substructure;
wherein,. DELTA.l 1 Is the real displacement component of the displacement sensor LVDT1 in the 4 displacement sensors;
Δl 2 is the real displacement component of the displacement sensor LVDT2 in the 4 displacement sensors;
Δl 3 the real displacement component of the displacement sensor LVDT3 in the 4 displacement sensors;
Δl 4 is the real displacement component of the displacement sensor LVDT4 in the 4 displacement sensors.
4. The real-time hybrid test method based on the combination of the vibration table and the actuator and the multi-degree of freedom loading as claimed in claim 3, wherein the 4 displacement sensors on the test substructure are arranged at the following positions:
the 4 displacement sensors are divided into two groups, wherein the displacement sensor LVDT1 and the displacement sensor LVDT2 are used as one group, the displacement sensor LVDT3 and the displacement sensor LVDT4 are used as the other group, the two groups of displacement sensors are respectively arranged on the third side surface and the fourth side surface of the test substructure, the displacement sensor LVDT1 and the displacement sensor LVDT2 are respectively arranged opposite to the actuator ChA and the actuator ChB, and the displacement sensor LVDT3 and the displacement sensor LVDT4 are respectively arranged opposite to the actuator ChC and the actuator ChD.
5. The base of claim 3The real-time hybrid test method combining the vibration table and the actuator and loading multiple degrees of freedom is characterized in that in the step S5, the real displacement of the test substructure comprises the real displacement d of the test substructure relative to the x direction in a ground coordinate system x "and the true displacement d of the test substructure relative to the y-direction in the ground coordinate system y And the implementation way to obtain the real displacement of the test substructure includes:
S51、Δl 1 、Δl 2 、Δl 3 and Δ l 4 The expressions are respectively:
wherein, L and S are respectively the length and the width of the test substructure; l 10 、l 20 、l 30 And l 40 The initial lengths of the displacement sensors LVDT1, LVDT2, LVDT3 and LVDT4 are respectively, and theta' is the real inclination angle of the test substructure relative to the ground;
s52, converting delta l 1 、Δl 2 、Δl 3 And Δ l 4 Expression simultaneous, obtaining d x ″、d y "and θ".
6. The method for the real-time hybrid test based on the combination of the vibration table and the actuator and the multi-degree-of-freedom loading as claimed in claim 3, wherein the target elongation delta l of the actuator ChA at any (i + 1) th moment A And actuated byTarget elongation Δ l of ChB B Target elongation Deltal of actuator ChC C And target elongation Δ l of actuator ChD D The expression of (a) is:
wherein, L and S are respectively the length and the width of the test substructure; l. the A0 、l B0 、l C0 And l D0 The initial lengths of actuator ChA, actuator ChB, actuator ChC and actuator ChD are shown.
7. The method as claimed in claim 1, wherein the restoring force R is corrected by a force correction strategy in combination with the model of the test substructure and the actual displacement of the test substructure in step S5 i+1 Obtaining a corrected restoring force R i ′ +1 The implementation mode of the method is as follows:
s51, the test substructure model is a linear model, the established test substructure model is Y, and a restoring force error delta R at the (i + 1) th moment is obtained according to the actual displacement difference of the test substructure at two adjacent moments and the actual speed difference of the test substructure at the two adjacent moments in the test substructure model Y E,i+1 (ii) a The two adjacent moments are the ith moment and the (i + 1) th moment respectively;
the speed 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, utilizing restoring force error delta R E,i+1 To actual restoring force R i+1 Compensating to obtain a corrected restoring force R i ′ +1 。
8. The real-time hybrid test method based on the combination of the vibration table and the actuator and the multi-degree-of-freedom loading as claimed in claim 1, wherein the motion equations of the two numerical substructures in the force correction state at the i-th moment are both:
M N a N,i +C N v N,i +K N d N,i ＝-M N a g -(R i +ΔR E,i )；
wherein, M N A quality matrix being a numerical substructure;
C N a damping matrix being a numerical substructure;
K N a stiffness matrix being a numerical substructure;
d N,i a displacement vector of the test substructure relative to the ground at the ith moment;
v N,i testing the velocity vector of the substructure relative to the ground at the ith moment;
a N,i testing the acceleration vector of the substructure relative to the ground at the ith moment;
a g the earthquake dynamic acceleration vector is obtained;
R i testing the actual restoring force of the substructure for the ith time;
ΔR E,i the restoring force error of the substructure is tested for time i.
9. The real-time hybrid test method based on the combination of the vibration table and the actuator and the multi-degree of freedom loading as claimed in claim 1, wherein in the step S4, the expression of the control law w of the sliding mode controller is as follows:
wherein,
C＝[01]；
p is a slip plane coefficient matrix, B * Is a first intermediate variable matrix, B is a first state space coefficient matrix, A is a second state space coefficient matrix, A * Is a second intermediate variable matrix, delta is a slip margin, C is a third intermediate variable matrix,
is a fourth intermediate variable, e EQ Error of actual equivalence power and equivalence power command, Z is state control model of control object, k 1 Is the internal model gain coefficient, and K is the state feedback gain coefficient. />
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