A method for evaluating shaking table-model structure interaction

Abstract

This invention provides a method for evaluating shaking table-model-structure interactions, including a formula-based evaluation method and a visual evaluation method for the interactions. The method includes the following steps: constructing a system model of the shaking table-model structure; analyzing the impact of the shaking table-model-structure interaction on the shaking table's control performance; deriving an interaction evaluation formula; performing a sensitivity analysis of the impact of model structure characteristics on the shaking table's control performance; and developing a visual evaluation standard for the interactions. This method can be used to assess the impact of shaking table-model-structure interactions in earthquake simulation shaking table tests, thereby enabling the adoption of different testing strategies.

Description

Technical Field

[0001] The invention belongs to the field of structural vibration testing, and in particular relates to an evaluation method for interaction between a vibration table and a model structure. Background Art

[0002] Earthquake simulation shake tables are widely used to test the dynamic characteristics of structures, verify the seismic resistance of equipment, and study the response characteristics and failure mechanisms of structures under earthquakes. However, due to the interaction between the shake table and the model structure, the accuracy of shake table tests can decrease to varying degrees. Assessing the impact of this interaction and determining appropriate testing strategies is a challenging issue in the field of structural testing technology. Summary of the Invention

[0003] To address the existing inability to assess the magnitude of interaction effects in shaking table tests, the present invention constructs a system model of the shaking table and model structure, based on the fundamental characteristics of the model structure and the shaking table system. This model then analyzes the magnitude of interaction effects under different model structure characteristics, and constructs an evaluation formula for the magnitude of interaction effects. By analyzing the sensitivity of different model structure characteristics to the effects of interaction and determining the magnitude of key characteristics, the interaction evaluation formula is further simplified, resulting in a visual interaction evaluation standard. This method is easy to implement and highly reliable, possessing practical significance and promising application prospects.

[0004] In one aspect, the present invention provides a shaking table-model structure interaction evaluation method that can effectively evaluate the interaction, including a formula evaluation method and / or a visual evaluation method, wherein the formula evaluation method and / or the visual evaluation method includes one or more of the following steps:

[0005] S1 acquires basic characteristic information of the vibration table and the model structure to a modeling computer, and the modeling computer constructs a system model of the vibration table-model structure;

[0006] S2 analyzes the effects of the interaction on the control performance of the shaking table based on the system model of the shaking table and the model structure under different model structure characteristic values;

[0007] S3 then determines the correlation between the interaction and the characteristic values of the model structure based on the system model of the shaking table and the model structure and the results of the influence of the interaction on the control performance of the shaking table;

[0008] S4 continues to analyze the sensitivity of different model structure characteristic values to the control performance of the shaking table based on the system model of the shaking table-model structure under different model structure characteristic values, and obtains key structure characteristic values and non-key structure characteristic values that affect the control performance of the shaking table;

[0009] S5 determines the values of non-critical characteristic values, and continues to judge the correlation between the interaction and the model structure characteristic values; and / or, determines the values of the key model structure characteristic values, plots the characteristic points in a rectangular coordinate system, and connects the characteristic points respectively, thereby forming a visual evaluation standard for the interaction.

[0010] Another aspect of the present invention provides a shaking table-model structure interaction evaluation system, which includes at least one processor and a memory storing instructions. When the instructions are executed by the at least one processor, the steps of the above method are implemented.

[0011] This invention provides a method for assessing the interaction between a vibration table and a model structure, which is easy to implement and highly reliable. Interaction assessment can be performed based on frequency-domain interaction response analysis. Furthermore, this method selects key characteristics that influence the interaction—the mass and eccentricity of the model structure—to effectively assess the impact of the interaction. Furthermore, based on the interaction assessment results, different test strategies can be adopted, which can help improve the accuracy of vibration table tests and can also serve as a basis for determining the implementation of interaction compensation strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 is a schematic diagram of the vibration table-model structure system of the present invention;

[0013] Figure 2 is a flow chart of the method for evaluating the interaction between the shaking table and the model structure according to the present invention;

[0014] Figure 3 It is a simplified diagram of the three-part model of the shaking table-structure system;

[0015] Figure 4 Schematic diagram of the vibration table and eccentric load system;

[0016] Figure 5 (a) Basic model of the dynamic model of the shaking table and eccentric load;

[0017] Figure 5(b) Equivalent model of the dynamic model of the shaking table and eccentric load;

[0018] Figure 5(c) Model construction of the dynamic model of the shaking table and eccentric load;

[0019] Figure 6 This is a standard diagram for visual evaluation of the interaction between the shaking table and the model structure according to the present invention.

[0020] Figure numerals: 1-model structure; 2-center of gravity of the model structure; 3-vibration table controller; 4-exciter 1; 5-exciter 2; 6-hydraulic cylinder; 7-servo valve; 8-center of gravity of the vibration table surface; 9-vibration table surface; 10-vibration table support; 11-guide device. DETAILED DESCRIPTION

[0021] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments provided herein are only used to illustrate the specific implementation process of the present invention and are not intended to limit the technical solutions of the present invention.

[0022] In some embodiments, the single horizontal dual-exciter vibration table (sometimes referred to as the vibration table) and the eccentric model structure are arranged eccentrically on the vibration table to simulate the situation where the eccentric model structure is arranged at the center of the vibration table surface. Figure 1 As shown, the center of gravity 2 of the model structure 1 is eccentrically arranged with the center of gravity 8 of the vibration table surface 9. The vibration table controller 3 controls the servo valve 7 and the hydraulic cylinder 6, thereby causing the exciter 1 (4) and the exciter 2 (5) to push the vibration table surface 9. The vibration table surface 9 also includes a connecting rod support 10 and a guide device 11.

[0023] In some embodiments, as Figure 2 As shown, a shaking table-model structure interaction evaluation method includes a formula evaluation method and / or a visual evaluation method, and the formula evaluation method and / or the visual evaluation method includes one or more of the following steps:

[0024] S1 acquires basic characteristic information of the vibration table and the model structure to a modeling computer, and the modeling computer constructs a system model of the vibration table-model structure;

[0025] S2 analyzes the effects of the interaction on the control performance of the shaking table based on the system model of the shaking table and the model structure under different model structure characteristic values;

[0026] S3 then determines the correlation between the interaction and the characteristic values of the model structure based on the system model of the shaking table and the model structure and the results of the influence of the interaction on the control performance of the shaking table;

[0027] S4 continues to analyze the sensitivity of different model structure characteristic values to the control performance of the shaking table based on the system model of the shaking table-model structure under different model structure characteristic values, and obtains key structure characteristic values and non-key structure characteristic values that affect the control performance of the shaking table;

[0028] S5 determines the values of non-critical characteristic values, and continues to judge the correlation between the interaction and the model structure characteristic values; and / or, determines the values of the key model structure characteristic values, plots the characteristic points in a rectangular coordinate system, and connects the characteristic points respectively, thereby forming a visual evaluation standard for the interaction.

[0029] Specifically, steps S1-S3 are "formula evaluation methods," which are not specifically limited in the present invention. Methods that derive an evaluation formula based on known theories are within the scope of the present invention. Steps S4-S5 are "visualization evaluation methods," which are not specifically limited in the present invention. Methods that simplify and evaluate the formula to obtain an evaluation curve are within the scope of the present invention.

[0030] In step S1, known methods for constructing a system model of a vibration table-model structure are all within the scope of the present invention. Figure 3 As shown, the system model constructed in step S1 for the vibration table-model structure primarily includes three components: a dynamic model (also known as a dynamic system model), a hydraulic drive model (also known as a hydraulic drive system model), and a three-parameter model (also known as a three-parameter control model). Based on these three components, a multi-input, multi-output model of the system can be constructed. During the construction of the dynamic model, the model structure and the vibration table can be treated as a single rigid body.

[0031] In some embodiments, the effects of the stiffness and damping of the vibration table surface and supporting links can be ignored during system model construction. A hydraulic drive model is established based on the hydraulic three-continuity equations. During the establishment of the three-parameter control model, the three-parameter control parameters must be debugged. Under no-load conditions, the three-parameter control parameters of the two vibrators of the vibration table are adjusted to ensure that their synchronization and tracking control performance are well aligned, and the characteristics of the two vibrators should be kept as consistent as possible.

[0032] The following example illustrates how to construct a vibration table-eccentric load system model when the model structure is an eccentric load.

[0033] 1. Dynamic modeling of vibration table and eccentric load

[0034] The schematic diagram of the vibration table and eccentric load (e.g. the main building of the new CCTV site) system is as follows: Figure 4 To simplify the analysis, the load is assumed to be rigid and is placed eccentrically on the vibration table to simulate the situation where the load's center of gravity deviates from the center of the vibration table. At the same time, the stiffness and damping between the vibration table and the connecting rod are not considered. The dynamic model of the vibration table and the eccentric load is as follows: Figure 5(a)-Figure 5(c) shown. Figure 5(a)-Figure 5(c) In the figure, E1 and E2 are two exciters respectively; A p p L1(F1) and A p p L2 (F2) are the outputs of the two exciters; x1 is the displacement of exciter 1; x2 is the displacement of exciter 2; M t is the mass of the vibration table surface; M s is the load mass; M e is the equivalent mass of the vibration table and the load; x is the displacement of the equivalent mass; J e is the equivalent moment of inertia of the vibration table and the load; φ is the motion angle of the equivalent moment of inertia; a is the eccentric distance of the equivalent mass; l is the distance from the exciter to the center of the vibration table surface.

[0035] Figure 5(a) shows the basic model of the vibration table and eccentric load, and Figure 5(b) shows its equivalent model. Using the construction method shown in Figure 5(c), the dynamic model of the vibration table and eccentric load can be obtained as follows:

[0036]

[0037] Where: J t and J s are the moments of inertia of the vibration table and the eccentric load itself; J t +J ta and J s +J sa are the moments of inertia due to the shaking table and the eccentric load relative to the x-axis in Figure 5(c), respectively.

[0038] 1.2 Dynamic system model, hydraulic drive system model, and three-parameter control model

[0039] Combined with the dynamic model, the force balance equation of the hydraulic drive system (dynamic system model) can be obtained as follows:

[0040]

[0041] Based on the constructed force balance equation and combined with the three continuity equations in Reference 1 (Wang Juke, Li Xiaojun, Li Fangfang, et al. Influence and compensation of interaction between unidirectional biaxial vibration table and structure [J]. Vibration and Shock, 2021, 40(10): 140-149.), the hydraulic system model of the vibration table and the eccentric load (hydraulic drive system model) can be obtained as follows:

[0042]

[0043] Based on the constructed hydraulic drive system model, and considering the influence of the three-parameter generator, three-parameter feedforward and feedback, and sensor, the system model of the vibration table and eccentric load (three-parameter control model) can be obtained as follows:

[0044]

[0045] Written in the form of transfer function matrix:

[0046]

[0047] Where: H 11 (H 12 ) is the transfer function of the exciter 1(2) affected by the interaction; H 12 (H 21 ) is the transfer function of the coupling effect of the two exciters affected by the interaction; u1(u2) is the control signal of exciter 1(2); H 11 、H 12 (H 21 ) and H 22 The expression is:

[0048]

[0049] Where: The expressions of G5, G6 and G7 are:

[0050]

[0051] Where: G3 is the transfer function of the three-parameter input device; G4 is the transfer function of the three-parameter feedback; G q k q is the transfer function of the servo valve; A p is the effective pressure-bearing area of the piston; G a is the transfer function of the sensor. Its expression and parameter values are detailed in references 1 and 2 (WANG Juke, LI Xiaojun, LI Fangfang, et al. Analysis of the interaction effects between double shaking tables and test structure[J]. Journal of Vibration and Control, 2021, 27(11-12): 1407-1419.).

[0052] In some embodiments of the present invention, in step S1, the basic characteristics of the vibration table and the model structure include the mass, moment of inertia, eccentricity and multi-exciter excitation of the model structure; and the system model of the vibration table-model structure is a multi-input multi-output system model.

[0053] In some embodiments of the present invention, in step S2, the term "model structure characteristic value" includes the mass ratio, moment of inertia ratio, eccentric distance ratio, etc. of the model structure and the vibration table, but the present invention is not limited thereto. "Model structure characteristic values" that need to be based on actual tests and do not exceed the working performance of the vibration table are all within the selection range of the present invention. The term "vibration table control performance" refers to the maximum function curve, acceleration spectrum characteristics, waveform distortion, table background noise, etc. of the vibration table, and here refers to the acceleration spectrum characteristics of the vibration table. When analyzing the impact of the interaction on the control performance of the vibration table, at least the magnitude and trend of the impact of the interaction on the control performance of the vibration table are analyzed and recorded.

[0054] In some embodiments of the present invention, in step S3, the expression of the interaction impact evaluation formula for determining the correlation between the interaction and the model structure characteristic value is:

[0055]

[0056] Where CSI(IRS) and CSI(MR) represent the interaction and the correlation between IRS and MR, respectively; f1 and f2 are functions of the interaction evaluation criteria, respectively; IRS is the ratio of the moments of inertia of the shaker and the system; IR is the ratio of the moments of inertia of the model structure and the shaker, also known as the moment of inertia ratio; ER is the ratio of the distance from the center of gravity of the model structure to the center of the shaker surface to the distance from the exciter to the center of the shaker surface, also known as the eccentric distance ratio; MR is the ratio of the mass of the model structure to the mass of the shaker surface, also known as the mass ratio.

[0057] In further explanation of some of the aforementioned embodiments of the present invention, in step S3, the influence of the system model and interaction based on the vibration table-model structure on the control performance focuses on the parameter selection of the interaction evaluation formula. Analysis of the constructed dynamic system model shows that the interaction between the vibration table and the model structure is mainly affected by the mass, moment of inertia, and degree of eccentricity of the model structure. The moment of inertia, degree of eccentricity, and mass of the model structure can be represented by the ratio of the moment of inertia of the vibration table to the system and the ratio of the mass of the model structure to the vibration table, respectively. Therefore, it can be assumed that the evaluation criteria for the interaction are:

[0058]

[0059] Where CSI(IRS) and CSI(MR) represent the interaction and the correlation between IRS and MR, respectively; f1 and f2 are functions of the interaction evaluation criteria, respectively; IRS is the ratio of the moments of inertia of the shaker and the system; IR is the ratio of the moments of inertia of the model structure and the shaker (moment of inertia ratio); ER is the ratio of the distance from the center of gravity of the model structure to the center of the shaker surface to the distance from the exciter to the center of the shaker surface (eccentricity ratio); and MR is the ratio of the mass of the model structure to the mass of the shaker surface (mass ratio).

[0060] In some embodiments of the present invention, the interaction impact evaluation formula is:

[0061]

[0062] Where: l is the distance from the exciter to the center of the vibration table; m is the length of the vibration table; n is the width of the vibration table;

[0063] In some preferred embodiments of the present invention: IR=0.1.

[0064] In further explanation of some of the aforementioned embodiments of the present invention, based on Equation 9 and combined with interaction analysis, the impact of interactions under different model structural characteristics can be evaluated, and different testing strategies can be adopted. If the interaction is not negligible, a control strategy must be adopted to compensate for the interaction; if the interaction is negligible, a shaking table test can be performed.

[0065] In some embodiments of the present invention, in step S4, the model structure characteristic values include mass, moment of inertia, and eccentricity.

[0066] In some embodiments of the present invention, Figure 6 As shown, in the step S5, the key characteristics and non-key characteristics determined in step S4 are combined, the parameter size of the non-key characteristics is determined based on actual experiments, and the interaction evaluation formula is further simplified; at the same time, combined with the influence of the interaction, the single variable principle is used to determine the value of the key characteristics respectively, the characteristic points are plotted in a rectangular coordinate system, and the characteristic points are connected to form a visual evaluation standard for the interaction.

[0067] In some embodiments of the present invention, a single variable method is used to determine the values of the key characteristics ER and MR:

[0068] First, set the value of ER to 0 and determine the value range of MR;

[0069] Secondly, based on the obtained MR value range, a specific MR value point is selected to determine the corresponding ER size and obtain the MR-ER point;

[0070] Finally, the obtained multiple MR-ER points are plotted in a plane rectangular coordinate system, and the characteristic points are connected respectively, so as to obtain a visual judgment standard for interaction impact evaluation.

[0071] In some embodiments of the present invention, when MR and ER vary, the control performance of the two exciters does not exceed ±3 dB in amplitude, and the effective frequency band is 70% or more of the effective operating frequency band.

[0072] In further explanation of some of the aforementioned embodiments of the present invention, in step S5, IR (model characteristics with low impact sensitivity) in the evaluation formula can be replaced with a constant. The selection criteria for this constant can be calculated based on commonly used model structures in shaking table tests; here, IR = 0.1. A single variable method can be used to determine the values of the key characteristics ER and MR: First, the value of ER is set to 0, and the range of MR values is determined. Second, based on the obtained MR range, specific MR value points are selected and the corresponding ER values are determined. Finally, the multiple (MR, ER) points (also called MR-ER points) obtained are plotted in a rectangular coordinate system, and the characteristic points are connected to obtain a visual judgment standard for interaction impact assessment. When determining the values of MR and ER, the following requirements can be set: when MR and ER vary, the control performance of the two exciters does not exceed ±3dB in amplitude, and the effective frequency band is 70% or above of the effective operating frequency band.

[0073] 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 evaluating shaking table-model structure interaction, characterized in that: The assessment methodology includes the following steps: S1 acquires basic characteristic information of the vibration table and the model structure to a modeling computer, and the modeling computer constructs a system model of the vibration table-model structure; S2 is based on the system model of the vibration table-model structure, analyzing the impact of the interaction on the vibration table control performance under different model structure characteristic values; S3 then determines the correlation between the interaction and the characteristic values of the model structure based on the system model of the shaking table and the model structure and the results of the influence of the interaction on the control performance of the shaking table; S4 continues to analyze the sensitivity of different model structure characteristic values to the control performance of the shaking table based on the system model of the shaking table-model structure under different model structure characteristic values, and obtains key structure characteristic values and non-key structure characteristic values that affect the control performance of the shaking table; S5: determining the values of non-critical characteristic values, and continuing to determine the correlation between the interaction and the model structure characteristic values; and / or determining the values of critical model structure characteristic values, plotting the characteristic points in a rectangular coordinate system, and connecting the characteristic points respectively, thereby forming a visual evaluation standard for the interaction; In step S3, the interaction impact evaluation formula for determining the correlation between the interaction and the model structure characteristic value is expressed as: Where: CSI(IRS) and CSI(MR) represent the interaction and the correlation between IRS and MR, respectively; f1 and f2 are functions of the interaction evaluation criteria, respectively; IRS is the ratio of the moments of inertia of the shaker and the system; IR is the ratio of the moments of inertia of the model structure and the shaker, also known as the moment of inertia ratio; ER is the ratio of the distance from the center of gravity of the model structure to the center of the shaker surface to the distance from the exciter to the center of the shaker surface, also known as the eccentric distance ratio; MR is the ratio of the mass of the model structure to the mass of the shaker surface, also known as the mass ratio; l is the distance from the exciter to the center of the shaker surface; m is the length of the shaker surface; n is the width of the shaker surface; IR=0.

1.

2. The method according to claim 1, characterized in that In step S1, the basic characteristics of the vibration table and the model structure include the model structure mass, moment of inertia, eccentricity, and multi-exciter excitation of the vibration table; the system model of the vibration table-model structure is a multi-input multi-output system model.

3. The method according to claim 2, characterized in that In the step S2, the model structure characteristic values include the mass ratio, moment of inertia ratio, and eccentric distance ratio of the model structure to the vibration table.

4. The method according to claim 1, characterized in that In the step S4, the model structure characteristic values include mass, moment of inertia, and eccentricity.

5. The method according to claim 4, characterized in that: In the step S5, the key characteristics and non-key characteristics determined in step S4 are combined, and the parameter sizes of the non-key characteristics are determined based on actual experiments to further simplify the interaction evaluation formula; at the same time, combined with the influence of the interaction, the single variable principle is used to determine the values of the key characteristics respectively, the characteristic points are plotted in a rectangular coordinate system, and the characteristic points are connected to form a visual evaluation standard for the interaction.

6. The method according to claim 5, characterized in that Use the single variable method to determine the values of key characteristics ER and MR: First, set the value of ER to 0 and determine the value range of MR; Secondly, based on the obtained MR value range, a specific MR value point is selected to determine the corresponding ER size and obtain the MR-ER point; Finally, the obtained multiple MR-ER points are plotted in a plane rectangular coordinate system to obtain a visual evaluation standard for interaction impact evaluation.

7. The method according to claim 6, characterized in that When MR and ER vary, the control performance of the two exciters does not exceed ±3dB in amplitude, and the effective frequency band is 70% or more of the effective operating frequency band.

8. A system for evaluating vibration table-model structure interaction, characterized in that: The system includes at least one processor and a memory, wherein the memory stores instructions. When the instructions are executed by the at least one processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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