A flexible multi-body dynamics method validated experimental device

Abstract

The application discloses a flexible multi-body dynamics method verification experimental device, which is used in the field of flexible multi-body dynamics experiments. The system comprises a structure system, a driving system, a measuring system and a connecting system. The structure system comprises a flexible test piece, an auxiliary beam and a counterweight piece. The driving system comprises a servo motor and a feedback control component thereof. The measuring system comprises an accelerometer, an angular displacement sensor, an eddy current sensor and a high-speed camera. The connecting system comprises equivalent torsional spring pieces and design modules for fixing two flexible beam test pieces together, and the system fundamental frequency of the flexible beam is adjusted by changing the torsional spring stiffness. The application provides a device for multi-section flexible beam dynamics experiments, which can accurately measure the displacement response and acceleration response of the test piece, is consistent with the modeling analysis results, and provides an important tool for related research and development.

Description

Technical Field

[0001] This invention belongs to the field of multibody system dynamics modeling and relates to an experimental device for verifying a flexible multibody dynamics method. Background Technology

[0002] Flexible multibody dynamics, as an emerging research direction, has broad application prospects in robotics, aerospace, automotive engineering, and other fields. However, the complexity and verification difficulty of flexible multibody dynamics modeling theory have always been a challenge and bottleneck in this field. Currently, scholars both domestically and internationally have made a series of advances in flexible multibody dynamics modeling theory, but how to verify these theories remains an urgent problem to be solved. Especially in the verification of multi-segment flexible beams, due to their complex structure and difficulty in measuring response, related experimental devices are currently scarce, particularly experimental devices for multiple flexible components, which are virtually nonexistent. Furthermore, the response measurement of large flexible beam experiments has always been a challenge; how to accurately measure its response is another important problem that needs to be solved in this field. Therefore, developing an experimental system that can effectively verify flexible multibody dynamics modeling theory is of great significance for the research and development of this field. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides an experimental apparatus for verifying flexible multibody dynamics methods, which can be used for verification research on flexible multibody dynamics modeling theory and simulation programs.

[0004] This invention provides an experimental apparatus for verifying flexible multibody dynamics methods, comprising:

[0005] The structural system includes a flexible flat beam test specimen, a high-stiffness follow-rotation auxiliary beam, and a counterweight. The test specimen is a flexible beam, and one end of both the test specimen and the auxiliary beam is fixed to the same axis so that the rotation angles at the root of the auxiliary beam and the test specimen are the same. A counterweight is provided at the free end of the test specimen.

[0006] The drive system drives the axis to move via a servo motor;

[0007] The measurement system includes an accelerometer, an angular displacement sensor, an eddy current sensor, and a high-speed camera;

[0008] The connection system includes an equivalent torsion spring sheet; the test piece comprises two sections, which are fixed together by the equivalent torsion spring sheet; the stiffness of the equivalent torsion spring sheet is changed to adjust the first-order bending frequency of the flexible beam.

[0009] In the structural system described, the flexible beam used in the experiment was a flexible beam segment made of metallic material as the test specimen, and an I-beam made of high-stiffness metallic material was selected as the auxiliary beam. Under the boundary condition of fixed support at one end, the first-order bending frequencies of the test specimen and the auxiliary beam differed by more than two orders of magnitude, so the elastic vibration of the auxiliary beam could be completely ignored. An eddy current meter installed on the auxiliary beam measured the lateral displacement of the flexible beam test specimen.

[0010] In the aforementioned drive system, a DC servo motor is connected to the shaft via a coupling, and the shaft's starting, stopping, or rotation according to a specific pattern is controlled by a servo control system. The shaft is mounted on a base via a bearing housing, and the motor is mounted on the base via a motor bracket.

[0011] In the measurement system described above, a high-speed camera is mounted on the top of the entire experimental setup to acquire video images of the test specimen during the experiment; accelerometers are mounted at several locations on the test specimen to measure the acceleration at the location of the test specimen; eddy current sensors are mounted on the auxiliary beam, near the root of the test specimen fixed to the shaft, to measure the lateral displacement of the test specimen; and angular displacement sensors are mounted on the shaft to measure the angular displacement of the shaft.

[0012] The connection system alters the stiffness of the equivalent torsion spring sheet, adjusting the first-order bending frequency of the flexible beam for studying different working conditions. The connection system also includes a design module for the equivalent torsion spring sheet, which models the flexible beam test specimen of this invention based on the equivalent torsion spring sheet. The transfer matrix method is used to quickly establish the flexible beam model, discretizing the flexible beam into a tree-like system composed of several massless beam segments, concentrated mass points, hinge supports, and tension / compression and torsion springs.

[0013] In a tree-like system, the state vector at coordinate x on the flexible beam is represented as Z(x) = [Y θ MQ]. T Where Y is deflection, θ is rotation angle, M is bending moment, Q is shear force, and the superscript T indicates transpose.

[0014] The changes in the state vector before and after each segment in a tree system are represented by transfer matrices, which include field transfer matrices, point transfer matrices, and point transfer matrices for hinges with torsion springs.

[0015] For a massless Bernoulli-Euler beam segment, the field transfer matrix is ​​[H]. F ] i as follows:

[0016]

[0017] For the intermediate stage, the i-th beam segment does not have a torsion spring hinge, and there is a general point transfer matrix [H]. S ] i as follows:

[0018]

[0019] The hinge with a torsion spring in the i-th beam segment has a transfer matrix [H]. Hinge ] i as follows:

[0020]

[0021] Based on the three matrices mentioned above, two theoretical simulation models can be constructed: a single-beam model and a double-beam model with torsion spring hinges. Compared to the finite element method, modeling is faster and facilitates parameter identification and analysis. The generalized eigenvalue f of the state vector of the tree system... i (k θ These are the system characteristic frequencies. The K characteristic frequencies f of the model tree system were measured through modal experiments. i exp Given i = 1, 2, ..., K, where K is a positive integer, find the objective function below to identify the equivalent stiffness k of the torsion spring sheet. θ ;

[0022]

[0023] Among them, f i (k θ ) is the i-th generalized eigenvalue of the system state vector.

[0024] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0025] (1) The device of the present invention realizes a dynamic experimental system for multi-segment flexible beams, which fills the domestic gap and provides a platform for verifying the dynamic modeling theory and simulation technology of flexible multibody;

[0026] (2) In order to overcome the inherent defects of a single measuring device, the device of the present invention selects four sets of measuring devices and adopts a multi-measurement data fusion method to capture experimental data, which is more accurate and can capture the complex characteristics of the power system more comprehensively.

[0027] (3) The connection system of the device of the present invention can adjust the first-order bending frequency of the flexible beam by changing the stiffness of the equivalent torsion spring sheet, so as to study different working conditions. At the same time, for the flexible beam test piece connected by the equivalent torsion spring sheet, the present invention can quickly establish two theoretical simulation models, namely a single beam and a double beam with a torsion spring hinge, based on the above-mentioned field transfer matrix, point transfer matrix and point transfer matrix of the hinge with torsion spring, making modeling faster; and based on the overall transfer matrix with unknown parameters, combined with modal test data and system identification methods, the equivalent stiffness of the torsion spring can be measured, which is convenient for parameter identification and analysis. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the overall structure of the experimental apparatus for verifying the flexible multibody dynamics method of the present invention.

[0029] Figure 2 This is a schematic diagram of the configuration of the experimental apparatus of the present invention during modal testing;

[0030] Figure 3 This is a schematic diagram of the servo drive control system of the present invention;

[0031] Figure 4 This is a schematic diagram of the eddy current meter calibration test principle of the present invention;

[0032] Figure 5 This is a comparison diagram of the simulated test trajectory of a certain measurement marker point in an embodiment of the present invention;

[0033] Figure 6 This is a graph showing the measurement results of the eddy current meter and its frequency domain processing results in an embodiment of the present invention;

[0034] Figure 7 This is a diagram showing the accelerometer measurement results and their frequency domain processing results in an embodiment of the present invention.

[0035] In the picture:

[0036] 1-Base; 2-Motor; 3-Motor bracket; 4-First coupling; 5-Bearing housing; 6-Shaft; 7-Second coupling;

[0037] 8-Angular displacement sensor bracket; 9-Angular displacement sensor; 10-First clamp; 11-Second clamp; 12-Cover plate;

[0038] 13-Auxiliary beam; 14-Eddy current meter; 15-Inner section of the test specimen; 16-Spring plate; 17-Outer section of the test specimen;

[0039] 18-Counterweight; 19-Finish light; 20-High-speed camera; 21-Clamp; 22-Level; 23-High-rigidity test specimen;

[0040] 24-Lifting platform; 25-Eddy current meter; 26-Laser displacement meter. Detailed Implementation

[0041] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0042] The experimental apparatus for verifying the flexible multibody dynamics method of this invention comprises a structural system, a drive system, a measurement system, and a connection system. The structural system includes a flexible experimental flat beam, a high-stiffness follower rotating auxiliary beam, and a counterweight; the drive system includes a servo motor and its feedback control components; the measurement system includes an accelerometer, an angular displacement sensor, an eddy current sensor, and a high-speed camera; and the connection system includes an equivalent torsional spring and its design method. For example... Figure 1-4 The diagram shows a specific structure implemented in an embodiment of the present invention.

[0043] (I) First, the structural system is described. The flexible beam used in the experiment was a segment of a metallic flexible beam as the test specimen, and an I-beam of high-stiffness metallic material was selected as the auxiliary beam to measure the lateral displacement response (deflection response) of the flexible beam. Under the boundary condition that one end of the test specimen was fixed, the first-order bending frequencies of the flexible beam and the auxiliary beam differed by more than two orders of magnitude; therefore, the elastic vibration of the auxiliary beam could be completely ignored. The eddy current meter mounted on the auxiliary beam was also able to capture the lateral displacement response of the experimental beam very well.

[0044] In the experiment, two conditions can alter the system's fundamental frequency (i.e., the first-order bending frequency)—the counterweight and the spring hinge. Since the accelerometer itself also has mass, it is necessary to analyze the effect of the concentrated mass point on the system's fundamental frequency.

[0045] Using the Dirac function, the concentrated mass at any position of the test beam is incorporated into the differential equation of the beam's transverse vibration:

[0046]

[0047] Where x is the beam displacement coordinate, y is the lateral vibration displacement, EI is the bending stiffness of the test beam, A is the beam cross-sectional area perpendicular to the neutral axis, ρ is the density of the test beam, n is the number of concentrated masses, and m j x j Here, f represents the mass and coordinates of the j-th concentrated mass, and f is the external force. This is the Dirac function.

[0048] If we only consider a beam that is fixed at one end and free at the other, with a concentrated mass m at the free end, then the frequency equation is as follows:

[0049] 1+coshβcosβ=α1β(coshβsinβ-sinhβcosβ)

[0050] in, l is the length of the test beam, and ω is the angular frequency of the beam's vibration.

[0051] The frequency equation is a transcendental equation and can be solved using numerical tools. The introduction of counterweights will directly affect the experimental and simulation results of rigid-flexible coupling and needs to be carefully considered in theoretical modeling. The influence of the spring hinge on the system frequency will be detailed in the section on connection systems.

[0052] like Figure 1 and Figure 2 As shown in this embodiment of the invention, in the structural system, the test piece comprises two sections. One end of the inner section 15 and one end of the outer section 17 are fixed together by an equivalent torsion spring plate 16. A counterweight plate 18 is provided at the other end of the outer section 17. The inner end of the inner section 15 is fixed to the shaft 6 by a first clamp 10, a second clamp 11, and a cover plate 12. One end of the auxiliary beam 13 is fixed to the shaft 6 to ensure that the rotation angle of the auxiliary beam 13 and the root of the test piece 15 is the same during the test. An eddy current sensor 14 is provided on the auxiliary beam 13 to measure the relative displacement change between the test piece 15 and the probe end face, i.e., the lateral displacement of the test piece.

[0053] (II) Description of the drive system of the present invention. The rotating shaft of this device is driven by a DC servo motor, and the servo control system controls the starting, stopping, or rotation of the rotating shaft according to a certain pattern.

[0054] like Figure 3 As shown, the servo control system structure used in the experiment of this embodiment of the invention includes a computer, a motion control card, a servo driver, and a servo motor. Figure 1 As shown, motor 2 is mounted on base 1 via motor bracket 3. Motor 2 is connected to shaft 6 via first coupling 4, driving shaft 6 to move. Shaft 6 is mounted on base 1 via bearing seat 5.

[0055] (III) Description of the Measurement System of the Present Invention. For measurement systems, devices capable of capturing large displacements often have insufficient sampling rates, making it difficult to capture the high-frequency displacement response at the end of elastic deformation; devices capable of capturing precise elastic responses often suffer from error accumulation or insufficient measurement range. Therefore, this invention selects four sets of measurement devices and employs a multi-measurement data fusion method to overcome the inherent defects of a single measurement device. The four sets of measurement devices selected in this invention are as follows:

[0056] (1) A high-speed camera is installed on the top of the entire experimental system to give full play to its advantages of non-contact measurement. It can collect displacement data of the flexible beam system over a wide range without interference. A high-speed camera is a device that can capture moving images with an exposure of less than 1 / 1000 second or a frame rate of more than 250 frames per second.

[0057] (2) Accelerometers are installed at the end of the flexible beam test piece to take full advantage of their high sampling rate and measure the acceleration response at key locations; there can be multiple accelerometers, which are arranged at multiple locations on the test piece;

[0058] (3) Eddy current meter, installed on the auxiliary beam, aligned with the root of the flexible beam test piece, fully utilizes its non-contact and high sampling rate characteristics to measure the deflection response at key locations;

[0059] (4) An angular displacement meter, which is fixedly connected to shaft 6, is used to calibrate and measure the angular displacement response of shaft 6.

[0060] like Figure 1 As shown, a high-speed camera 20 is installed on the top of the entire experimental system to capture video images of the test specimen during the experiment; several accelerometers are arranged at any position on the test specimens 15 and 17 and their coordinate positions are recorded; an eddy current meter 14 is installed on the auxiliary beam 13 and aligned with the root of the flexible beam test specimen; an angular displacement sensor 9 is fixed on the angular displacement sensor bracket 8 and connected to the shaft 6 through the second coupling 7 to measure the rotation angle of the test specimen and the auxiliary beam on the shaft 6 during the experiment.

[0061] Before the test, the eddy current meter 14 needs to be calibrated. Figure 4 As shown, a high-rigidity test specimen 23 is supported by a horizontal lifting platform 24, and a level 22 is used to ensure that the beam plane remains horizontal during the lifting process. The lateral displacement of the rigid beam test specimen 23 is measured using an eddy current meter 25 and a laser displacement meter 26, respectively. The functional relationship between the measuring voltage of the eddy current meter 14 and the longitudinal displacement is obtained, thus enabling the determination of the lateral displacement. Figure 1 The lateral displacement of the test piece can be determined by measuring the voltage of the eddy current meter in the experimental setup shown.

[0062] (iv) The connection system of the present invention will be described below. The connection system consists of, as follows: Figure 1 and Figure 2 The system comprises a first clamp 10, a second clamp 11, and a spring plate 16. The first clamp 10 and the second clamp 11 ensure that the root of the flexible beam test specimen can be completely fixed to the shaft 6. The spring plate 16 is introduced to adjust the fundamental frequency of the system by changing the stiffness of the spring plate, thus allowing for the study of various working conditions. The connection system also includes a design module for an equivalent torsional spring plate. This module models the flexible beam test specimen of the present invention based on the equivalent torsional spring plate, and uses the transfer matrix method to quickly establish a tree system of flexible beam models.

[0063] Tree-structured systems can be used to quickly model and analyze flexible beams using the transfer matrix method. Based on the beam's properties, the state vector of the beam section is a 4×1 matrix. The state vector at coordinate x on the flexible beam is Z(x) = [Y θ MQ]. TWhere Y is deflection, θ is rotation angle, M is bending moment, and Q is shear force. The superscript T indicates transpose.

[0064] Any tree-shaped beam system can be discretized into a system consisting of several massless beam segments, concentrated mass points, hinged supports, tension / compression and torsion springs, etc. In this system, the change of the system's state vector Z(x) before and after each segment can be represented by the transfer matrix, namely the field transfer matrix and the point transfer matrix.

[0065] For a massless Bernoulli-Euler beam segment, the field transfer matrix is ​​as follows:

[0066]

[0067] In this context, the superscripts L and R represent the left and right ends of the beam, respectively. EI represents the length of the i-th beam segment. i Represents the bending stiffness of the i-th beam segment, denoted by [H]. F ] i It is the field transfer matrix.

[0068] For intermediate steps, there is a general point transfer matrix [H] S ] i as follows:

[0069]

[0070] In the formula, m i J is the concentrated mass of the i-th beam segment. i Let k be the lumped inertia of the i-th beam segment. t,i k is the tension / compression spring stiffness of the i-th beam segment. r,i It is the torsional spring stiffness of the i-th beam segment. It is the eccentric mass of the i-th beam segment, e i It is the eccentricity of the i-th beam segment.

[0071] For a hinge with a torsion spring, there is a transfer matrix {H}. Hinge} i as follows:

[0072]

[0073] Where, k θ This indicates the equivalent stiffness of the torsion spring.

[0074] Based on the three matrices mentioned above, two theoretical simulation models can be constructed: a single beam and a double beam with torsion spring hinges. Compared to the finite element method, modeling is faster and facilitates parameter identification and analysis. For example, for a double beam model with an accelerometer (lumped mass) at the end, its overall transfer function model is Z(X... n)=[H F ]1[H Hinge ]1[H F ]2[H S ]1Z(X 0 The generalized eigenvalues ​​f of the system's state vector i (k θ This is the system characteristic frequency, where i = 1, 2, ..., K, and K is a positive integer. Let the experimentally measured system frequency be f. i exp Searching for k θ Make

[0075]

[0076] Thus, the equivalent stiffness k of the torsion spring can be identified. θ X 0 X n These are the coordinates of the root and tip of the tree system, Z(X) 0 Z(X) n These are the root state vector and the tip state vector of the tree system, respectively.

[0077] Example

[0078] 1. Select 7075 aluminum alloy flexible experimental beams A1, B1, and C1 with rectangular cross sections, 700 mm long, 50 mm high, and 1 mm, 1.5 mm, and 2 mm thick, and experimental beams A2, B2, and C2 with a length of 300 mm and other parameters identical, as well as beams A3, B3, and C3 with a length of 1000 mm and other parameters identical.

[0079] 2. Modal tests were conducted to identify the equivalent torsional stiffness of the spring sheet. Taking the flexible beam A1+A2 as an example, its fixed-support first-order bending mode frequency is 0.734Hz, while the first-order bending mode frequency of the auxiliary beam is 108.253Hz, which is much larger than that of the flexible beam test specimen. Simultaneously, through transfer function calculation and modeling, the torsional stiffness k of the spring sheet in this experiment was identified. θ = 0.15 N·m / rad;

[0080] 3. Assemble the experimental equipment and install the measurement module:

[0081] 3.1) Use clamps to fix flat beams A and B onto the rotating shaft according to the transverse placement scheme;

[0082] 3.2) Set up a high-speed camera at a predetermined position above the test specimen and connect it to the measurement network; set up an artificial light source; and affix artificial markers to the predetermined position on the test specimen;

[0083] 3.3) Install the eddy current meter on the auxiliary beam, aligning it with one side of the root of the flexible beam;

[0084] 3.4) Fix the accelerometer at the midpoint of the length of the outer flexible beam test piece, fix the wires in sections along the flexible beam in a non-tensioned state with glue, and pull them to the base and connect them to the control computer.

[0085] 4. Given the input to the motor controller, control the rotation of the test piece, and use a computer to record the measured strain and the image sequence data captured by the high-speed camera;

[0086] 5. Disassemble flat beams A and B and reinstall them according to the longitudinal placement plan;

[0087] 6. Repeat steps 2-5;

[0088] 7. Disassemble the test specimens and measuring equipment;

[0089] 8. Process the experimentally measured data to obtain the displacement and acceleration responses at the measured locations of the test specimen, and compare them with the results of the established flexible multibody dynamics modeling and analysis. One set of displacement data from the measured points is shown below. Figure 5 As shown in the figure, solid lines represent the simulation results of the x-coordinate in the ground coordinate system, and dashed lines represent the simulation results of the y-coordinate; hollow dots represent the experimental measurement results of the x-coordinate, and solid dots represent the experimental measurement results of the y-coordinate. Other eddy current meter measurement results and their frequency domain processing results are as follows... Figure 6 As shown, the accelerometer measurement results and frequency domain processing results are as follows: Figure 7 As shown, this invention can provide multiple data sources for the verification of flexible multibody dynamics simulation theories and programs, including absolute displacement of measurement points, acceleration response, and beam root deflection response, which can be used for various analyses in the time and frequency domains. Simultaneously, the structural system can utilize test specimens of different stiffnesses and numbers, as well as equivalent torsion springs with different torsional stiffnesses and counterweights of different masses, to meet the multi-condition verification requirements of various theories.

[0090] Except for the technical features described in the specification, all other technologies are known to those skilled in the art. Descriptions of well-known components and technologies are omitted in this invention to avoid redundancy and unnecessary limitation. The above embodiments are only for illustrating the technical concept and features of this invention, and are intended to enable those skilled in the art to understand the content of this invention and implement it accordingly. They should not be construed as limiting the scope of protection of this invention. All equivalent changes or modifications made according to the spirit and essence of this invention should be covered within the scope of protection of this invention.

Claims

1. An experimental apparatus for verifying a flexible multibody dynamics method, characterized in that, It includes a structural system, a drive system, a measurement system, and a connection system; The structural system includes a test piece, an auxiliary beam, and a counterweight. The test piece is a flexible beam, and one end of both the test piece and the auxiliary beam is fixed to the same axis so that the rotation angles at the roots of the auxiliary beam and the test piece are the same. A counterweight is provided at the free end of the test piece. The drive system drives the axis to move via a servo motor; The measurement system includes: a high-speed camera mounted on the top of the entire experimental setup to acquire video images of the test specimen during the experiment; an accelerometer mounted on the test specimen to measure the acceleration at the location of the test specimen; an eddy current sensor mounted on an auxiliary beam near the root of the test specimen where it is fixed to the shaft to measure the lateral displacement of the test specimen; and an angular displacement sensor mounted on the shaft to measure the angular displacement of the shaft. The connection system includes an equivalent torsion spring sheet; the test piece comprises two sections, which are fixed together by the equivalent torsion spring sheet; the stiffness of the equivalent torsion spring sheet is changed to adjust the first-order bending frequency of the flexible beam. The connection system also includes a design module for an equivalent torsion spring sheet. This module uses the transfer matrix method to model the flexible beam test piece, discretizing the flexible beam into a tree system consisting of several massless beam segments, concentrated mass points, hinge supports, tension and torsion springs. In a tree-like system, the state vector at coordinate x on the flexible beam is represented as: Where Y is the deflection, Let M be the rotation angle, M be the bending moment, Q be the shear force, and the superscript T indicate transpose; The changes in the state vector before and after each segment in a tree system are represented by a transfer matrix, which includes a field transfer matrix, a point transfer matrix, and a point transfer matrix for hinges with torsion springs. For the i-th beam segment, the field transfer matrix is... as follows: ； The i-th beam segment does not have a torsion spring hinge and has a general point transfer matrix. as follows: ； The i-th beam segment has a torsion spring hinge and a point transfer matrix. as follows: ； In this context, the superscripts L and R represent the left and right ends of the beam, respectively, and the subscripts i and i+1 represent the i-th beam segment and the (i+1)-th beam segment, respectively. This represents the length of the i-th beam segment. Let represent the bending stiffness of the i-th beam segment. It is the concentrated mass of the i-th beam segment. It is the lumped inertia of the i-th beam segment. It is the tension / compression spring stiffness of the i-th beam segment. It is the torsional spring stiffness of the i-th beam segment. It is the eccentric mass of the i-th beam segment. ω is the eccentricity of the i-th beam segment, and ω is the angular frequency of the beam vibration. This indicates the equivalent stiffness of a torsion spring. Simulation models of a single beam and a double beam with a torsion spring hinge were constructed based on the transfer matrix; the system frequency was measured experimentally, and the equivalent stiffness of the torsion spring was then identified.

2. The experimental apparatus according to claim 1, characterized in that, In the structural system described, the test piece is a flexible beam made of metallic material, and the auxiliary beam is an I-beam made of high-stiffness metallic material. Under the boundary condition that one end of the flexible beam and the auxiliary beam is fixedly supported, the first-order bending frequencies of the flexible beam and the auxiliary beam differ by more than two orders of magnitude.

3. The experimental apparatus according to claim 1 or 2, characterized in that, In the aforementioned structural system, the test piece comprises an inner section and an outer section. One end of the inner section is fixed to one end of the outer section via an equivalent torsion spring. A counterweight is provided at the other end of the outer section. The other end of the inner section is fixed to a shaft via a clamp and a cover plate. One end of the auxiliary beam is also fixed to the shaft.

4. The experimental apparatus according to claim 1, characterized in that, In the drive system described above, a DC servo motor is connected to the shaft via a coupling, and the shaft is controlled by a servo control system to start, stop, or rotate according to a set pattern; the shaft is mounted on a base via a bearing housing, and the motor is mounted on the base via a motor bracket.

5. The experimental apparatus according to claim 1, characterized in that, In the aforementioned measurement system, the eddy current sensor is calibrated before the experiment to obtain the functional relationship between the eddy current sensor's measurement voltage and the lateral displacement of the test piece.

6. The experimental apparatus according to claim 1, characterized in that, The connection system also includes a clamp for fixing the root of the test piece to the shaft.

7. The experimental apparatus according to claim 1, characterized in that, The connection system also includes a design module for an equivalent torsion spring sheet. This module establishes a double-beam model with a torsion spring hinge for the two-section structure of the test piece, with an accelerometer at one end. The overall transfer function model of the tree-like system is as follows: ,in These refer to the root and tip positions of the tree system, respectively. , These are the state vectors at the corresponding positions. , These are the field transfer matrices for the first and second beam segments, respectively. This is the point transfer matrix of the first beam segment with a torsion spring hinge. It is the point transfer matrix of the first beam segment; K characteristic frequencies of the model tree system were measured through modal experiments. Given i = 1, 2, ..., K, where K is a positive integer, find the objective function below to identify the equivalent stiffness of a torsion spring sheet. ; in, It is the i-th generalized eigenvalue of the system state vector.

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