A method for analyzing interaction between a double shaking table array and a test structure

Abstract

The present application relates to a kind of double shaking table and the interaction influence analysis method and device of test structure, the system model of double shaking table and test structure is established, and based on the system model constructed, the CSI (control-structure interaction) influence under different shaking table working conditions is in-depth studied, the influence of CSI on single shaking table, the coupling between two shaking tables, the influence of double shaking table array synchronization, tracking control performance is analyzed and revealed.Compared with the previous assumption that two shaking tables are the same, the CSI influence is reduced, the synchronization performance is seriously degraded, and the measured frequency of the structure is reduced.In addition, the present application also provides a method for how to form double shaking table array in actual shaking table test.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of vibration test, and particularly relates to a double vibration table array and a test structure interaction influence analysis method. BACKGROUND

[0002] Electro-hydraulic vibration table is an important experimental equipment for reproducing actual vibration environment, and is widely used in fields such as engineering earthquake test, aerospace vibration test, automobile road simulation, etc. In the vibration table test, the control structure interaction (CSI) refers to the dynamic coupling effect between the vibration table and the test structure. The CSI not only affects the control accuracy of the vibration table, but also brings errors to the response of the test structure. In the face of the CSI influence between the single vibration table and the test structure, the related technology has been comprehensively studied. However, few studies involve the CSI influence between the double vibration table and the test structure, and the influence of the interaction on the measured frequency of the structure. The control structure interaction (CSI) between the double vibration table array and the test structure is an important reason for the decline of the vibration table test accuracy. At present, the existing technology has not involved the following two important aspects: the interaction between the two different vibration tables and the test structure and the influence of the interaction on the measured frequency of the structure. SUMMARY

[0003] In order to solve the above technical problems, the present application provides a double vibration table and test structure interaction influence analysis method, the double vibration table includes vibration table 1 and vibration table 2, vibration table 1 includes servo valve 1, hydraulic cylinder 1, exciter 1, vibration table table 1, vibration table 2 includes servo valve 2, hydraulic cylinder 2, exciter 2, vibration table table 2, wherein the system model used by the method is shown in formula (11):

[0004]

[0005] Wherein, x1 is the displacement of exciter 1, x2 is the displacement of exciter 2, u 01 is the control signal of vibration table 1, u 02 is the control signal of vibration table 2, G5, G6, G7, G8, G9 and G 10 As shown in formula (9):

[0006]

[0007] Wherein, M1 is the mass of vibration table 1, M2 is the mass of vibration table 2, C is the damping coefficient of test structure, s represents Laplace operator, K is the stiffness coefficient of test structure, M S is the mass of test structure, k q1 G q1 is the transfer function of servo valve 1, k q2 G q2is the transfer function of servo valve 2, G a1 and G a2 is the transfer function of sensor, G 41 and G 42 is the feedback of two TVCs, A P1 and A P2 is the effective area of two hydraulic cylinders, G 21 and G 22 The analytical expression of is shown in equation (4):

[0008]

[0009] Where V1 and V2 are the total volume of two hydraulic cylinders, K C1 and K C2 is the flow pressure parameter near the steady state operating point, C C1 and C C2 is the total leakage coefficient of hydraulic cylinder, and β represents the effective volume modulus respectively.

[0010] Further, the interaction analysis method of double shaking table and test structure, wherein the transfer function matrix converted by equation (11) is shown in equation (12):

[0011]

[0012] Where the expressions of H11, H12, H12 and H22 are shown in equation (13):

[0013]

[0014] Where H11 and H22 are the transfer functions of two exciters affected by CSI, and H12 and H21 are the transfer functions of coupling between two actuators.

[0015] Further, the interaction analysis method of double shaking table and test structure, wherein the system model is constructed by considering three sub-models of dynamic model, hydraulic drive model and TVC model.

[0016] Further, the interaction analysis method of double shaking table and test structure, wherein the dynamic model is shown in equation (1):

[0017]

[0018] Where M1 and M2 are the masses of two shaking table surfaces respectively, F1 is the output of exciter 1, F2 is the output of exciter 2, x1 is the displacement of exciter 1, x2 is the displacement of exciter 2, M S is the mass of test structure; x S is the displacement of test structure, C is the damping coefficient of test structure, and K is the stiffness coefficient of test structure;

[0019] The displacement of the test structure is shown in equation (2):

[0020]

[0021] where M S is the mass of the test structure; x S is the displacement of the test structure, K is the stiffness coefficient of the test structure, s represents the Laplace operator, x1 is the displacement of the exciter 1, and x2 is the displacement of the exciter 2

[0022] Further analysis method of the interaction between the double shaking table and the test structure, wherein the hydraulic drive model is shown in equation (3):

[0023]

[0024] where k q1 G q1 and k q2 G q2 are the transfer functions of the two servo valves, u1 and u2 are the control error signals of the two shaking tables, A P1 and A P2 are the effective areas of the two hydraulic cylinders.

[0025] Further analysis method of the interaction between the double shaking table and the test structure, wherein the TVC model is shown in equation (5):

[0026]

[0027] where u 01 and u 02 are the control signals of the two shaking tables, G 31 and G 32 are the generators and feedforward of the two TVCs, G 41 and G 42 are the feedbacks of the two TVCs, G a1 and G a2 are the transfer functions of the sensors.

[0028] Further analysis method of the interaction between the double shaking table and the test structure, wherein the transfer functions of the sensors are shown in equation (6):

[0029]

[0030] where n a1 and n a2 are the frequencies of the sensors, D a1 and D a2 are the damping ratios of the sensors.

[0031] The second aspect of the present application further provides a computer readable storage medium for analyzing interaction influence of a double vibration table and a test structure, which stores program instructions executable by a processor to implement the steps of the foregoing method.

[0032] The third aspect of the present application further provides a computer device for analyzing interaction influence of a double vibration table and a test structure, which comprises a memory, a processor and program instructions stored in the memory and executable by the processor, wherein the processor executes the program instructions to implement the steps of the foregoing method.

[0033] The present application has the beneficial effect that the present application establishes a system model of a double vibration table and a test structure, based on the constructed system model, the CSI influence under different vibration table working conditions is tested in depth, and the influence of CSI on a single vibration table, the coupling between two vibration tables, the synchronization of a double vibration table array and the tracking control performance is revealed. Compared with the previous assumption that two vibration tables are the same, the CSI influence is reduced, the synchronization performance is seriously degraded, and the measured frequency of the structure is reduced. In addition, the present application also provides a method for how to form a double vibration table array in an actual vibration table test. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a schematic diagram of a double vibration table and a test structure;

[0035] Figure 2 is a schematic diagram of a system model of a double vibration table array and a test structure;

[0036] Figure 3 is a schematic diagram of a vibration table 1;

[0037] Figure 4 is a schematic diagram of a vibration table 2;

[0038] Figure 5 is a schematic diagram of the influence of interaction on a transfer function matrix;

[0039] Figure 6 is a schematic diagram of the influence of interaction on a vibration table;

[0040] Figure 7 is a schematic diagram of the influence of interaction on a vibration table array;

[0041] Figure 8 is a schematic diagram of the influence of interaction on a test structure. DETAILED DESCRIPTION

[0042] The following examples further illustrate the present application, but should not be construed as limiting the present application. Modifications or substitutions to the method, steps or conditions of the present application, without departing from the spirit and essence of the present application, all belong to the scope of the present application.

[0043] The related art studies the influence of CSI on different system models under different system characteristics with two identical shakers and a test structure. The related art analyzes the influence of CSI on the shaker and test structure (MST) model, the servo valve flow demand model, the exciter output demand model, and the structure resonance response model under different structure characteristics. The analysis shows the influence trend and degree of CSI on these models. The related art studies the influence of mechanical installation error, displacement measurement error, and servo valve bias on the MST. The study shows that the internal force of the double shaker system increases with the increase of these characteristics, and these factors reduce the control performance of the double shaker. At the same time, the related art also points out that the synchronization control error of the double shaker increases with the increase of the equivalent load mass difference between the two shakers, and decreases with the increase of the stiffness of the test structure. The related art gives the influence of redundant force and external disturbance force on the control performance of the double shaker in a study. The study shows that the redundant force and external disturbance force will affect the MST. The related art analyzes the amplitude-frequency response characteristics of the double shaker and test structure system, and the analysis result shows that there is a large coupling effect between the two shakers. The related art analyzes the influence of CSI on the control performance of the double shaker under different test structure characteristics. The analysis shows that the coupling effect between the two shakers increases with the increase of the influence of CSI. The related art studies the influence of CSI on the test precision of the shaker, and the study shows that CSI has a great influence on the test precision.

[0044] The above related art shows that the influence of CSI between two identical shakers and a test structure is only analyzed. However, in actual shaker tests, the characteristics of the two shakers are completely different. Therefore, the system model constructed in the past cannot reflect the real characteristics of the double shaker and test structure system. In addition, the synchronization and tracking control performance of the double shaker is a very important index, but the existing research has not involved it. In addition, the past research mainly focuses on the time domain response of the structure, and does not pay attention to the influence of CSI on the frequency domain response of the test structure. Therefore, the existing research needs to be further expanded.

[0045] In view of the above research deficiencies, the embodiments of the present application take two completely different shakers and a test structure as the research object, and construct a system model thereof. Based on the system model, the influence of CSI is deeply tested.

[0046] 1. System model construction of double shaker and test structure

[0047] Figure 1 A schematic diagram of the double shaker and test structure is shown in FIG. 1. The double shaker and test structure mainly consists of a TVC controller (three-parameter controller, real-time control computer), servo valve 1 and servo valve 2, hydraulic cylinder 1 and hydraulic cylinder 2, exciter 1 and exciter 2, shaker table 1 and shaker table 2, and test structure. It can be observed from FIG. 1 that the two shakers are connected in series through the test structure, and the test structure is connected to the two shakers through the hydraulic cylinders. Figure 1It can be seen that the system is driven horizontally by two different vibration tables. Therefore, the two different vibration tables are coupled with each other, and the system model is a multi-input multi-output model.

[0048] according to Figure 2 The system model was established using a modular approach as shown. This approach divides the system model into three submodels: a dynamic model, a hydraulic drive model, and a TVC model. These submodels represent the system's kinematic mechanism, hydraulic drive, and control components. During the system modeling process, the composition and physical properties of these three submodels were comprehensively considered. The system composition and physical properties are described below in the dual-shake table array and test structure. A detailed explanation of the symbols will be provided in the modeling process.

[0049] 1.1 Dual vibration table array and test structure

[0050] 1.1.1 Basic Introduction of Vibration Table 1

[0051] Vibration table 1 Figure 3 Its performance indicators and parameters are given in Tables 1 and 2.

[0052] Table 1. Basic performance of vibration table 1

[0053]

[0054] Table 2. System parameters of vibration table 1

[0055]

[0056] 1.1.2 Basic Introduction of Vibration Table 2

[0057] Vibration table 2 Figure 4 Its performance indicators and parameters are given in Tables 3 and 4.

[0058] Table 3. Basic performance of vibration table 2

[0059]

[0060] Table 4. System parameters of vibration table 2

[0061]

[0062] 1.1.3 Introduction to the test structure

[0063] The basic properties of the test structure are determined according to the actual test. As can be seen from Table 1 and Table 3, the maximum load of the two shaking tables is 10000kg and 5000kg, respectively. Therefore, the mass of the test structure should not exceed twice the maximum load capacity of shaking table 2 (10000kg). According to the conclusion that the greater the mass of the test structure, the greater the impact of the CSI. Finally, the mass of the test structure is determined to be 9000kg. The damping ratio and frequency of the test structure are determined according to the characteristics of the actual civil structure. The basic parameters of the test structure are shown in Table 5.

[0064] Table 5. Basic parameters of the test structure

[0065]

[0066] 1.2. Dynamic system modeling

[0067] The dynamic model of the dual shaking table and the test structure is shown in Figure 2 Figure 1, where the English meanings are as follows: Dynamic model, test structure, shaking table-1, shaking table-2. The detailed explanation of the symbols in the figure is as follows: M1 and M2 are the masses of the two shaking table surfaces, respectively, F1 is the output of the exciter 1, F2 is the output of the exciter 2, x1 is the displacement of the exciter 1, x2 is the displacement of the exciter 2, M S is the mass of the test structure; x S is the displacement of the test structure, C is the damping coefficient of the test structure, and K is the stiffness coefficient of the test structure.

[0068] According to Newton's second law, the dynamic model is

[0069]

[0070] where s represents the Laplace operator.

[0071] According to the modeling process in the reference (Huang, H. H. Design and application of the shaking table (Seismological Press, Beijing, 2008), the displacement of the test structure is

[0072]

[0073] 1.3 Hydraulic drive and TVC system modeling

[0074] According to the modeling process of the hydraulic driving system introduced in the reference (Wang, J., et al. Differential movement synchronous tracking control strategy of double-shaking table system loading with specimen. Shock. Vib. 2018, 1-11 (2018)), the hydraulic driving model is

[0075]

[0076] where k q1 G q1 and k q2 G q2 are the transfer functions of two servo valves, u1 and u2 are the control error signals of two shaking tables, A P1 and A P2 are the effective areas of two hydraulic cylinders, G 21 and G 22 are the analytical expressions of k q1 G q1 and k q2 G q2

[0077]

[0078] Based on the modeling process of the TVC system given in the reference (Wang, J., Li, X., Li, F. & Li, N. Analysis of the interaction effects between double shaking tables and test structure. J Vib Control 27(11-12), 1407-1419 (2021)), the TVC model of the double shaking table and the test structure can be obtained. The control error signal is:

[0079]

[0080] where u 01 and u 02 are the control signals of two shaking tables, G 31 and G 32 are the generators and feedforward of two TVCs, G 41 and G 42 are the feedbacks of two TVCs, G a1 and G a2 are the transfer functions of sensors. The expression of the sensor transfer function is:

[0081]

[0082] where na1 and n a2 is the frequency of the sensor, D a1 and D a2 is the damping ratio of the sensor.

[0083] 1.4 System modeling

[0084] Based on the above three sub-models of dynamic system modeling, hydraulic drive and TVC system modeling, the analysis model of the double shaking table and the test structure is established. Combining formulas (1) and (3), the following can be obtained:

[0085]

[0086] Bringing formulas (5) and (6) into formula (7), the model of the system can be obtained as:

[0087]

[0088] Assume

[0089]

[0090] The following can be obtained:

[0091]

[0092] Finally, the system model of the double shaking table and the test structure can be obtained as:

[0093]

[0094] Converting formula (11) into the transfer function matrix shown below, the following can be obtained:

[0095]

[0096] Where H11 and H22 are the transfer functions of the two exciters affected by CSI, and H12 and H21 are the transfer functions of the coupling between the two actuators, and the expressions of H11, H12, H12 and H22 are as follows:

[0097]

[0098] Assume u 01 = u 02 = u, then the transfer functions of the two exciters are as follows:

[0099]

[0100] Where A1 is the transfer function of exciter 1, and A2 is the transfer function of exciter 2.

[0101] Based on the modeling process described above, the system model of the double shaking table and the test structure is obtained. The parameters of the system model are listed in Section 1.1. These parameters have actual physical meaning and are determined according to actual engineering.

[0102] 2. Analysis of the influence of CSI on the shaking table

[0103] Based on the constructed system model, the influence of CSI on the double shaking table is studied in depth. The study is carried out under different shaking table conditions. Specifically, the two shaking tables are 1.0m x 1.0m shaking table and 3.0m x 3.0m shaking table. The characteristics of the two shaking tables are given in Section 1.1. Table 6 gives different shaking table conditions.

[0104] Table 6. Different shaking table conditions

[0105]

[0106] In order to comprehensively study the influence of CSI, the following three aspects are analyzed respectively: the influence of CSI on the transfer function matrix, the single shaking table and the double shaking table. In order to compare and analyze the influence of CSI, the condition [1] (two 1.0m x 1.0m shaking tables empty) is defined as the reference condition. In the analysis, the amplitude-frequency characteristic of the shaking table is a key indicator, and if the indicator value is within ±3.00dB, it means that the shaking table will work within its effective frequency range.

[0107] 2.1 Influence of interaction on the transfer function matrix

[0108] Figure 5 The influence of CSI on the transfer function of shaking table 1 is given. It can be seen from Figure 5 (a) that peak and trough effects occur at the frequencies of the test structure and its surrounding band. Specifically, at 4.58Hz, the value of H11 under condition [2] (1-1 shaking table and test structure) is 19.40dB, and at 4.79Hz, the value of H11 under condition [2] is -11.30dB. At 4.80Hz, the value of H11 under condition [3] (1-3 shaking tables and test structure) is 5.53dB, and at 5.03Hz, the value of H11 under condition [3] is -5.12dB. According to the above data, the two peak-to-valley values can be calculated as 30.70dB and 10.65dB, and the average values of the two frequency points corresponding to the peak-to-valley values are 4.67Hz and 4.92Hz, respectively. The above calculation results show that if the two shaking tables are different, the amplitude of the peak and trough is reduced by about 10 times, and the frequency is slightly increased.

[0109] From Figure 5It can be seen from (b) that the H12 value of [2] (1-1 shaker and test structure) is 19.20 dB at 4.58 Hz, and the H12 value of [3] (1-3 shakers and test structure) is 3.73 dB at 4.86 Hz. These data show that the coupling between the two shakers reduces by about 5.94 times, if the slight difference in frequency is not considered.

[0110] In addition, from Figure 5 It can be seen that the influence of CSI on the transfer function matrix is consistent with that of the biaxial shaker. This consistency proves the correctness of the system modeling and the rationality of the above results.

[0111] 2.2 Influence of interaction on single shaker

[0112] The influence of CSI on single shaker is studied in frequency domain and time domain respectively. The seismic motion El Centro NS with peak acceleration of 342.00 cm / s 2 was used, and was compressed by 3 times to form the time domain input signal.

[0113] Figure 6 The influence of CSI on single shaker is given. From Figure 6 (a), it can be seen that the S1 value of [2] (1-1 shaker and test structure) is 25.30 dB at 4.58 Hz, and the S1 value of [2] is -12.90 dB at 5.01 Hz. The S1 value of [3] (1-3 shakers and test structure) is 10.40 dB at 4.86 Hz, and the S1 value of [3] is -7.06 dB at 5.15 Hz. According to the above data and Figure 5 , it can be concluded that when the two shakers are different, the amplitude of the peak and the trough decreases, and the frequency increases slightly. The coupling effect between the two shakers makes the peak and trough effect more obvious. In addition, the peak and trough amplitudes in both cases exceed the range of ±3.00 dB, which means that the shaker will not work in the effective frequency range.

[0114] Figure 6 (b)-(d) of (b) shows the influence of CSI on the time domain waveform reproduction performance of the 1.0 m x 1.0 m shaker and test structure system. Figure 6 (b) of (b) shows the reproduction of seismic motion record, Figure 6 (c) of (b) shows the evaluation index of reproduction, Figure 6 (d) of (b) shows the Fourier spectrum of the reproduction record. In order to facilitate observation and comparison, the reproduction from 2.0 s to 2.4 s and the Fourier spectrum from 2.0 Hz to 8.0 Hz are enlarged respectively.

[0115] FromFigure 6 As can be seen from (b), at 2.20s, the reproduction results of vibration table 1 are 495.30cm / s 2 and -29.50 cm / s 2 , the reproduction result of the reference signal is 5.40cm / s 2 These data prove that if the two vibration tables are the same, the waveform reproduction is amplified by about 17.79 times at 2.20s. In order to evaluate the waveform reproduction performance in the full time domain, Figure 6 (c) gives three quantitative indicators: correlation coefficient, MAX(e) and RMSE. Figure 6 As can be seen from (c), the correlation coefficients are 52.34% and 78.15%, MAX(e) are 70.45dm and 50.92dm, and RMSE are 86.49% and 66.75%. Based on the above data, it can be seen that if the two vibration tables are different, the RMSE will be reduced by 19.74%. Figure 6 (d) shows that at 4.40 Hz, the Fourier spectrum value of the input signal is 59.21 cm / s 3 At 4.60, under the working condition [2] (1-1 vibration table and test structure), the output Fourier spectrum value is 183.00cm / s 3 At 4.40 Hz, under the working condition [3] (1-3 vibration table and test structure), the output Fourier spectrum value is 80.82 cm / s 3 These data indicate that if the two shakers were different, the interaction would be reduced by 102.18 cm / s 3 .observe Figure 6 From (d), we can see that peak and trough effects also appear at the natural frequency of the structure and its surrounding frequency bands, which is consistent with Figure 7 The above consistency shows the rationality of the analysis results.

[0116] 2.3 Effects of interaction on shaking table array

[0117] Synchronization and tracking control errors are two important performance indicators of a dual shaker array. Figure 7 The synchronization and tracking control errors of the dual vibration table array and the test structure are given. Figure 7 (a) shows that the maximum synchronization control error between two different vibration tables is 473.20 cm / s 2 , if the two vibration tables are identical, the synchronization control error is 0. Figure 8 (b) shows that at 2.20s, the tracking control error of the two vibration tables is 498.80cm / s 2 The tracking control error of the two vibration tables is 23.96cm / s. 2These data prove that at time 2.20, the synchronization control error will increase significantly and the tracking control error will decrease by about 95.20%.

[0118] 2.4 Effects of interactions on experimental structure

[0119] In a shaking table test, the response of the structure is of primary interest. Figure 8 The influence of CSI on the response of the test structure is given. Figure 8 (a) gives the response of the test structure, Figure 8 (b) shows the Fourier spectrum of the response. For easy observation and comparison, the reproduction from 2.0s to 2.4s and the Fourier spectrum from 2.0Hz to 8.0Hz are magnified respectively.

[0120] By comparison Figure 8 From the response in the 0-10s range in (a), it can be concluded that if the two vibration tables are the same, the response of the structure will be amplified. At 2.20s, the ideal test response value is -954.10cm / s 2 ;[2](1-1 vibration table and test structure) The response under working condition is; -2899.00cm / s 2 ;[3](1-3 vibration table and test structure) The response under working condition is 170.70cm / s 2 From the above data, it can be seen that at 2.20s, the response under the [2] condition is about 3.04 times the ideal test response. The results show that the influence of CSI is amplified in previous studies using two identical vibration tables and test structures.

[0121] from ​ (b) shows that at 5.00 Hz, the Fourier value of the reference condition is 483.40 cm / s 3 ; At 4.60Hz, the Fourier spectrum value of the working condition [2] (1-1 vibration table and test structure) is 1176.00cm / s 3 ; At 4.90Hz, the Fourier spectrum value of working condition [3] (1-3 vibration table and test structure) is 717.70cm / s 3 The following comparison can be made based on the resonant frequency points under different conditions: If the two vibration tables are identical, the percentage error between the measured value and the actual value (structural frequency) is 8%. If the two vibration tables are different, the percentage error is 2%. This comparison shows that the CSI effect introduces errors into the measured frequency of the structure. If the two vibration tables are different, the percentage error between the measured value and the actual value decreases under the vibration table conditions.

[0122] In summary, the present invention establishes a system model between a dual vibration table array and a test structure, tests the interaction effect under different vibration table working conditions, and obtains the effect of CSI on the response of the vibration table and the test structure. The technical effects produced include: Compared with the traditional research assuming that the two vibration tables are identical

[0123] 1. The impact of CSI on a single shaker is reduced, and the system's waveform reproduction and tracking performance are improved;

[0124] 2. The synchronization performance of the dual shaker array is severely reduced, which may cause damage to the test structure and the shaker array;

[0125] 3. The measured frequency of the test structure changes. The magnitude of the change depends on the characteristics of the two shakers and the magnitude of the CSI effect. The more similar the characteristics of the two shakers, the more significant the change in the measured frequency.

[0126] 4. In actual shaker tests, it is difficult to simultaneously reduce the CSI effect and improve synchronization performance. Therefore, when constructing a dual shaker array, a large shaker should be used whenever possible.

[0127] The embodiments and functional operations of the subject matter described in this specification may be implemented in digital electronic circuitry, tangibly implemented computer software or firmware, computer hardware including the structures disclosed in this specification and their structural equivalents, or a combination of one or more of the foregoing. The embodiments of the subject matter described in this specification may be implemented as one or more computer programs, i.e., as one or more modules of computer program instructions encoded on one or more tangible, non-transitory program carriers, for execution by, or to control the operation of, a data processing device.

[0128] Alternatively or additionally, the program instructions may be encoded on an artificially generated propagated signal, such as a machine-generated electrical, optical, or electromagnetic signal, which is generated to encode information for transmission to an appropriate receiver device for execution by a data processing device. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of the foregoing.

[0129] Although the present invention has been described in detail above using general explanations, specific embodiments, and experiments, it will be apparent to those skilled in the art that modifications and improvements may be made based on the present invention. Therefore, such modifications and improvements, which do not depart from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A method for analyzing the interaction influence of a double vibration table and a test structure, the double vibration table comprising a vibration table 1 and a vibration table 2, the vibration table 1 comprising a servo valve 1, a hydraulic cylinder 1, an exciter 1, a vibration table table top 1, the vibration table 2 comprising a servo valve 2, a hydraulic cylinder 2, an exciter 2, a vibration table table top 2, wherein, The system model used in the method is shown in equation (11): where x1 is the displacement of shaker 1, x2 is the displacement of shaker 2, u 01 is the control signal of shaker 1, u 02 is the control signal of shaker 2, G5, G6, G7, G8, G9 and G 10 As shown in equation (9): Where M1 is the mass of vibration table 1, M2 is the mass of vibration table 2, C is the damping coefficient of the test structure, s represents the Laplace operator, K is the stiffness coefficient of the test structure, and M S is the mass of the test structure, k q1 G q1 is the transfer function of servo valve 1, k q2 G q2 is the transfer function of servo valve 2, G a1 and G a2 is the transfer function of the sensor, G 31 and G 32 are the generator and feedforward of two TVCs, G 41 and G 42 is the feedback of two three-parameter (TVC), A P1 and A P2 is the effective area of ​​the two hydraulic cylinders, G 21 and G 22 The analytical expression of is shown in formula (4): where V1 and V2 are the total volumes of the two hydraulic cylinders, K C1 and K C2 are the flow-pressure parameters near the steady operating point, C C1 and C C2 are the total leakage coefficients of the hydraulic cylinders, and β represents the effective bulk modulus, respectively. The system model is constructed by considering three sub-models of dynamic system model, hydraulic drive model and three-variable control (TVC) model; The dynamic system model is shown in equation (1): where M1 and M2 are the masses of the two shakers' tables, F1 is the output of shaker 1, F2 is the output of shaker 2, x1 is the displacement of shaker 1, x2 is the displacement of shaker 2, M S is the mass of the test structure; x S is the displacement of the test structure, C is the damping coefficient of the test structure, and K is the stiffness coefficient of the test structure. The displacement of the test structure is shown in equation (2): where M S is the mass of the test structure; x S is the displacement of the test structure, K is the stiffness coefficient of the test structure, s denotes the Laplace operator, x1 is the displacement of the exciter 1, and x2 is the displacement of the exciter 2; The hydraulic drive model is shown in equation (3): where M1 is the mass of the shaker 1, M2 is the mass of the shaker 2, k q1 G q1 and k q2 G q2 are the transfer functions of the two servo valves, u1 and u2 are the control error signals of the two shakers, A P1 and A P2 are the effective areas of the two hydraulic cylinders; The TVC model is shown in equation (5): where: u 01 and u 02 are the control signals of the two shakers, G 31 and G 32 are the generators and feedforward of the two TVCs, G 41 and G 42 are the feedbacks of the two TVCs, G a1 and G a2 are the transfer functions of the sensors.

2. The method of claim 1, wherein, The transfer function matrix converted from equation (11) is shown in equation (12): Wherein, the expressions of H11, H12, H12 and H22 are shown in equation (13): Wherein, H11 and H22 are the transfer functions of the two exciters affected by CSI, and H12 and H21 are the transfer functions of the coupling between the two actuators.

3. The method of claim 1, wherein the test structure is a structure to be tested, and the test structure is a structure to be tested. The expression of the transfer function of the sensor is: where: n a1 and n a2 are the frequencies of the sensor, D a1 and D a2 are the damping ratios of the sensor.

4. A computer readable storage medium for interaction analysis of a double vibration table and a test structure, which stores program instructions executable by a processor to implement the steps of the method of any one of claims 1-3.

5. A computer device for interaction analysis of a double vibration table and a test structure, comprising a memory, a processor and program instructions stored in the memory and executable by the processor, wherein the processor executes the program instructions to implement the steps of the method of any one of claims 1-3.

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