A vibration simulation feedback method for reproducing displacement
By measuring and adjusting the motor output of the mechanical drive test device in real time, the high-precision displacement reproduction of the bridge model under wind-induced vibration is achieved, and the problem that traditional mechanical drive devices cannot simulate multimodal coupling and multi-frequency coupling vibration is solved, and the accuracy and stability of the simulation are improved.
Patent Information
- Application Number
- CN202210895262.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-07-26
- Publication Date
- 2025-03-18
- Estimated Expiration
- 2042-07-26
AI Technical Summary
When traditional mechanical drive devices simulate bridge wind-induced vibration, they cannot reproduce the displacement time course with high accuracy, and can only achieve single-mode vibration, and cannot simulate bridge vibrations with multi-mode coupling and multi-frequency coupling.
A vibration simulation feedback method is used to measure the model displacement in real time, compare it with the target displacement time course, and adjust the motor output according to the error to ensure that the model displacement is consistent with the target displacement. The method includes placing the free vibration test device and the mechanically driven test device in the flow field, measuring the model motion time, calculating the error, and adjusting the motor output according to the error, so as to achieve accurate reproduction of the displacement.
High-precision displacement simulation under the action of incoming flow is realized, and bridge vibrations of multi-modal coupling and multi-frequency coupling can be reproduced, improving the accuracy and stability of the simulation.
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Figure CN115307867B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of vibration simulation, and in particular to a vibration simulation feedback method for reproducing displacement. Background Art
[0002] As the span of modern bridges continues to expand, stiffness and damping also decrease. This leads to a dynamic response that increases with the span under various external forces, namely bridge vibration. Among various external forces, the influence of wind is the most frequent and significant, and wind-induced bridge vibration often occurs in long-span bridges. This vibration can cause instability of the bridge structure and fatigue damage of the structure.
[0003] Wind-induced vibration of long-span bridges has become an issue that must be considered during design and construction. Reproduction of wind-induced response of bridges is a very important topic in bridge wind engineering.
[0004] At present, the wind-induced response of bridges can be reproduced through free vibration tests and mechanical drive tests. In the free vibration test, the model is fixed by elastic suspension, and the model vibrates under the action of the incoming flow. The mechanical drive test uses a motor to apply a forced force to make the model move. The free vibration test uses an external load excitation to obtain the displacement, which cannot be accurately controlled, has a large test error, and is non-repeatable. Using mechanical drive to simulate free vibration can improve the signal-to-noise ratio and make signal recognition more stable. Reproducing the free vibration displacement time history through mechanical drive, retaining the self-excitation force effect during the simulation process, achieving repeated reproduction of the free vibration test and accurate measurement of the self-excitation force, is conducive to in-depth research on bridge vibration phenomena.
[0005] The traditional mechanical drive device applies load to the bridge segment model through a servo motor to achieve the target displacement. Among the patents that have been published, the patent document (CN102607800A) discloses a decoupled three-degree-of-freedom bridge segment model forced vibration system. The system can achieve complete decoupling of three-degree-of-freedom motion, and each degree of freedom can independently achieve simple harmonic motion with adjustable frequency, phase, and amplitude. However, the system has certain limitations: it can only perform single-mode vibration; and the control system is force control, and the displacement control accuracy under the action of the incoming flow is poor.
[0006] At present, traditional mechanical drive devices have the following disadvantages:
[0007] (1) The operation accuracy is unreliable. The traditional mechanical drive device only applies a specified force to the segment model to make it reach the target displacement. This is a one-way control without feedback. As a result, when there is an incoming flow, the self-excitation force of the bridge caused by the incoming flow will also affect the displacement of the bridge segment model, causing the displacement to deviate from the target value;
[0008] (2) The simulated vibration mode is single. In terms of motion form, the traditional mechanical drive device adopts a force-controlled motor drive method, which can only achieve simple harmonic vibration drive in different degrees of freedom and cannot reproduce a variety of possible wind-induced vibration forms, including multi-mode coupling and multi-frequency coupling bridge vibration.
[0009] In summary, traditional mechanical drive devices cannot simulate the real vibration of bridges under actual wind fields, which inevitably produces large errors and affects the results of scientific research analysis.
[0010] Therefore, in order to solve the above problems, it is necessary to provide a mechanical drive test method that can achieve high-precision displacement simulation and multi-modal coupled vibration. Summary of the invention
[0011] The objectives of the present invention are achieved through the following technical solutions.
[0012] In view of the deficiencies of the existing problems, the present invention provides a vibration simulation feedback method for reproducing displacement, which solves the problem that the model displacement time history of the current traditional mechanical drive device deviates from the target displacement time history under the action of the incoming flow.
[0013] Specifically, the present invention provides a vibration simulation feedback method for reproducing displacement, comprising the following steps:
[0014] (1) placing a free vibration test device and a mechanical drive test device in a flow field, and operating the free vibration test device and the mechanical drive test device;
[0015] (2) The target motion time of the first bridge segment model in the free vibration test device is recorded as A d ;
[0016] (3) At time i, measure the motion time history A(t i );
[0017] (4) Calculate A(t i ) and A d (t i ) has an error of E;
[0018] (5) According to the positive or negative value of E, determine whether to increase or decrease the motor output; if E < 0, increase the motor output; if E > 0, reduce the motor output; if E = 0, keep the motor output unchanged;
[0019] (6) The motor outputs a forced force acting on the second bridge segment model in the mechanical drive test device, and the motion state of the model changes;
[0020] (7) Determine whether all target schedules have been achieved. If not, set i = i + 1 and repeat from step (3);
[0021] (8) Finally, the displacement of the second bridge segment model in the mechanical drive test device is made the same as the target value of the motion time course.
[0022] Further, the free vibration test device comprises a first bridge segment model and an elastic suspension system, and the first bridge segment model is mounted on the elastic suspension system;
[0023] The mechanical drive test device includes a second bridge segment model, a vertical motor motion track, a lateral motor motion track, and a torsion motor motion track; the second bridge segment model is connected and fixed to the torsion motor motion track.
[0024] Furthermore, the elastic suspension system is assembled from eight identical springs, wherein two of the springs are connected in series to form four identical spring strings and are suspended, and each spring string has the same height;
[0025] Every two of the spring strings form a pair of spring strings, the two pairs of spring strings are symmetrically placed on both sides of the first bridge segment model, and the middle of each pair of spring strings is connected by a first connecting shaft;
[0026] The middle parts of the two first connecting shafts are connected by a second connecting shaft, and the first bridge segment model is connected and fixed at the middle position on the second connecting shaft.
[0027] Furthermore, the mechanical drive test device further includes three groups of motors, which are vertical motion motors, lateral motion motors and torsional motion motors, respectively controlling the motion of three degrees of freedom; wherein,
[0028] The vertical motion motor is installed on the vertical motor motion track, the lateral motion motor is installed on the lateral motor motion track, and the torsion motion motor is installed on the torsion motor motion track.
[0029] Furthermore, the mechanical drive test device includes a base and brackets fixedly installed on both sides of the base, and a first slider installed on the brackets for sliding in a horizontal direction, a second slider installed on the first slider for sliding in a vertical direction, and the second bridge segment model installed rotationally between the second sliders are installed between the brackets, and the second bridge segment model vibrates in one or more of the three degrees of freedom of horizontal, vertical and rotational directions.
[0030] Furthermore, the bracket is provided with the horizontal motor motion track in the horizontal direction, the first slider is slidably installed on the horizontal motor motion track, the first slider is provided with the vertical motor motion track in the vertical direction, and the second slider is slidably installed on the vertical motor motion track.
[0031] Furthermore, the bracket is provided with the lateral motion motor for driving the first slider to slide in the horizontal direction and the vertical motion motor for driving the second slider to slide in the vertical direction, and the second slider is provided with the torsional motion motor for driving the second bridge segment model to rotate.
[0032] Furthermore, the rotation axis of the second bridge segment model is arranged perpendicular to the horizontal direction and the vertical direction respectively.
[0033] Furthermore, a plurality of feedback encoders are fixedly mounted on the bracket for real-time feedback of the output displacement time course.
[0034] Furthermore, the vibration form of the second bridge segment model in each degree of freedom is any one of the following motions: single-frequency simple harmonic motion, simple harmonic motion with multiple frequencies superimposed, motion with frequency varying over time, motion with amplitude varying over time, motion with mean varying over time, and random motion.
[0035] The advantages of the present invention are:
[0036] (1) The displacement-reproducible mechanical drive device is different from the traditional mechanical drive device in that it can control the magnitude of the output force through the real-time displacement error, thereby ensuring that the model displacement time history does not deviate from the target displacement time history;
[0037] (2) Through the displacement feedback system, the new mechanical drive device can retain the self-excitation effect during the simulation process and reproduce the displacement response of the free vibration structure and the development characteristics of the self-excitation force. In this test, the forcing force provided by the mechanical drive device is the same as the sum of the damping force and elastic restoring force of the free vibration test;
[0038] (3) Since the displacement reproduction type mechanical drive device no longer relies on the motor drive of simple force control, but can simulate any displacement time history within the threshold range through displacement feedback. Therefore, the new mechanical drive device can realize steady-state and non-steady-state motion forms, the former including single-frequency simple harmonic and multi-frequency coupled simple harmonic motion; the latter including time-varying frequency, time-varying amplitude and random vibration. Through the closed-loop feedback control method, the device can operate with high precision and stability under the condition of incoming flow interference, and realize the simulation of multi-degree-of-freedom complex motion forms of the bridge main beam section under special wind conditions. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:
[0040] Attached Figure 1 A schematic diagram of the principle of a free vibration test device according to an embodiment of the present invention is shown.
[0041] Attached Figure 2 A schematic diagram of the principle of a mechanical drive test device according to an embodiment of the present invention is shown.
[0042] Attached Figure 3 A schematic diagram of a single-degree-of-freedom oscillator model in a free vibration test according to an embodiment of the present invention is shown.
[0043] Attached Figure 4 A schematic diagram of a single-degree-of-freedom oscillator model in a mechanical drive test according to an embodiment of the present invention is shown.
[0044] Attached Figure 5 A schematic diagram of the three-dimensional structure of a mechanical drive test device according to an embodiment of the present invention is shown.
[0045] Attached Figure 6 A partial structural schematic diagram of a mechanical drive test device according to an embodiment of the present invention is shown.
[0046] Attached Figure 7 A flow chart of a vibration simulation method for reproducing model displacement according to an embodiment of the present invention is shown. DETAILED DESCRIPTION
[0047] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.
[0048] According to an embodiment of the present invention, a vibration simulation feedback system for reproducing displacement is proposed. In the present invention, the displacement reproduction type mechanical drive test method measures the model displacement in real time, adjusts the motor output size with the free vibration displacement time history as the target displacement, thereby changing the forcing force in real time to make the model displacement consistent with the target displacement.
[0049] Among them, the existing free vibration test devices, such as Figure 1As shown, it includes a bridge segment model 1 and an elastic suspension system 2. The elastic suspension system 2 is assembled from eight identical springs, wherein two springs are connected in series to form four identical spring strings and are suspended, and each spring string has the same height. Every two spring strings form a pair of spring strings, and the two pairs of spring strings are symmetrically placed on both sides of the bridge segment model 1, and the middle of each pair of spring strings is connected by a first connecting shaft. The middle parts of the two first connecting shafts are connected by a second connecting shaft. The bridge segment model 1 is connected and fixed to the middle position on the second connecting shaft.
[0050] The mechanical drive test device used in this application is as follows: Figure 2 As shown, it includes a bridge segment model 1, a vertical motor motion track 3, a horizontal motor motion track 4, and a torsion motor motion track 5. The bridge segment model 1 is connected and fixed to the middle position of the torsion motor motion track 5.
[0051] The displacement reproduction mechanical drive test can retain the self-excitation effect in the simulation process and reproduce the development characteristics of the displacement response and self-excitation of the free vibration model. Figure 3 , 4 The principle is:
[0052] For a single-degree-of-freedom oscillator model placed in a fluid, the model motion will excite the self-excited force of the fluid acting on the model;
[0053] In the free vibration test, the forces acting on the model include: inertia force F m , self-excitation force F se , Restoration F k , damping force F c In the mechanical drive test, the forces acting on the model include: inertia force F m , self-excitation force F se , Force F f ;
[0054] When the mechanically driven test reproduces the displacement of the free vibration model, the two test models are subjected to the same total external forces, the same inertial forces, and the same self-excited forces;
[0055] Therefore, the forcing force exerted by the motor on the model in the mechanical drive test is equal to the sum of the restoring force and the damping force exerted on the model in the free vibration test.
[0056] In the free vibration wind tunnel model test, the model motion is independent of each other in three degrees of freedom: vertical, lateral, and torsional.
[0057] The mechanical drive test device further includes three sets of motors, namely vertical motion motor, lateral motion motor and torsional motion motor, which respectively control the motion of three degrees of freedom. The motion trajectories in different directions are constrained by independent limit tracks, see Figure 2 , the vertical motion motor is installed on the vertical motor motion track, the lateral motion motor is installed on the lateral motor motion track, and the torsion motion motor is installed on the torsion motor motion track. At the same time, the coupling between different degrees of freedom is realized. The synchronous control of the motion of different degrees of freedom is guaranteed by a unified time axis. The magnitude of the output forced force is determined hour by hour through a displacement reproduction type vibration simulation feedback system.
[0058] The entire mechanical drive system consists of wind-model-mechanical drive device. The mechanical drive device is installed on the model and placed in the wind tunnel laboratory. The fan is started to simulate the wind environment encountered by the bridge, and the mechanical drive device is started to drive the model to vibrate, simulate the target displacement time history, and study the forced force and self-excited force time history of the bridge model under stable forced motion.
[0059] Attached Figure 5 The three-dimensional structure schematic diagram of the mechanical drive test device according to the embodiment of the present invention is shown. The test device comprises a base 10 and brackets 20 fixedly mounted on both sides of the base, a first slider 30 slidably mounted on the bracket along a first direction, a second slider 40 slidably mounted on the first slider along a second direction, and a bridge segment model 50 rotatably mounted between the second sliders are installed between the brackets, and the test device vibrates in one or more of the three degrees of freedom of the first direction, the second direction and the rotation.
[0060] Attached Figure 6 The schematic diagram of the partial structure of the mechanical drive test device according to the embodiment of the present invention is shown. Specifically, the bracket 20 in the present embodiment is provided with a first guide rail 21 along the first direction (horizontal direction), the first slider 30 is slidably mounted on the first guide rail 21 (the horizontal motor motion track 4), and the first slider 30 is provided with a second guide rail 31 along the second direction (vertical direction) (i.e. Figure 2 The second slider 40 is slidably mounted on the second guide rail 31, and the first direction and the second direction are arranged perpendicular to each other.
[0061] The bracket 20 is provided with a first driving device 61 (i.e., a lateral motion motor in FIG. 2 ) for driving the first slider 30 to slide in the first direction and a second driving device 62 (i.e., a lateral motion motor in FIG. 2 ) for driving the second slider 40 to slide in the second direction. Figure 2 The second slider 40 is also provided with a third driving device 63 (i.e. Figure 2 The torsional motion motor in the segment model 50 is arranged perpendicular to the first direction and the second direction respectively.
[0062] Preferably, the first drive device 61 and the second drive device 62 are linear motors, which directly provide horizontal and vertical motion power for the segment model. Compared with the traditional ball screw, it has no intermediate transmission mechanism, simplifies the system, greatly improves the accuracy, adopts a coreless structure, has no cogging force, has stable motion, and is light in weight.
[0063] The first guide rail 21 and the second guide rail 31 are linear guide rails, and adopt P-level precision guide rails with small friction, high rigidity, and parallel accuracy of up to 2μm. They provide guidance in the horizontal and vertical directions and play a fixing role.
[0064] The third driving device 63 is a DD motor, which provides rotational power for the segment model. It adopts a direct drive design concept, has no intermediate transmission and reduction mechanism, and has an accuracy of up to 0.7 degrees.
[0065] Furthermore, a plurality of feedback encoders 64 are fixedly mounted on the bracket 20 for real-time feedback of the output displacement time series. The feedback encoder is mainly composed of a reading head and a relative grating scale with a resolution of ±0.001 mm. The main function is to provide real-time feedback of the output displacement time series. The returned data is used for comparison with the target displacement, and any deviation can be adjusted in real time.
[0066] The vibration form of the segment model of the mechanical drive test device in the present invention in each degree of freedom is any one of the following motions: single frequency simple harmonic motion, simple harmonic motion with multiple frequencies superimposed, motion with frequency varying over time, motion with amplitude varying over time, motion with mean varying over time, and random motion. The variable parameters of each vibration form include vibration time, vibration frequency, vibration amplitude, etc. The realization of these vibration forms can be realized in the three degrees of freedom of lateral, vertical and torsional directions respectively.
[0067] Different degrees of freedom of the mechanical drive test device can be combined with each other, including any two-by-two combinations and three-degree-of-freedom combinations. There are 7 combinations (see Table 1). The coupling includes: lateral alone, vertical alone, torsion alone, lateral + vertical, lateral + torsion, vertical + lateral, lateral + vertical + torsion. Each degree of freedom is controlled separately, and different degrees of freedom do not interfere with each other.
[0068] Table 1: Coupling between different degrees of freedom
[0069] Number of degrees of freedom coupling Coupling form Single degree of freedom Lateral, vertical, torsional Two degrees of freedom Lateral + vertical, vertical + torsion, lateral + torsion Three degrees of freedom Lateral + vertical + torsion
[0070] The coupling principle between the three degrees of freedom is as follows:
[0071] 1) Control of single degree of freedom motion. The entire test device has a total of 6 motors (2×3, controlling 3 degrees of freedom on the left and right sides respectively) and 4 guide rails (2×2, vertical and lateral motion on the left and right sides, and no guide rails are required for torsional motion). For lateral and vertical motion, each degree of freedom is powered by its corresponding linear motor, and its own guide rail provides guidance and fixation; for torsional motion, the corresponding DD motor provides the power for rotation, and the rotation axis is the middle axis of the DD motor. From the above description, it can be seen that different degrees of freedom have their own corresponding power supply (linear motor or DD motor) and motion constraints (guide rails or rotating shafts), which are independently controlled and not interfered by other degrees of freedom. Since the 6 degrees of freedom on the left and right are controlled by their own corresponding motors, the smooth realization of motion depends on the complete synchronous control of the corresponding degrees of freedom on the left and right sides.
[0072] 2) Coupling between different degrees of freedom: coupling between different degrees of freedom or coupling between three degrees of freedom is achieved through coupling of guide rails.
[0073] In the present invention, different vibration forms are realized by the type of input signal; the length of the running time is controlled by the length of the input signal. The longer the input signal length is, the longer the running time is. For example, the input signal time history has a total of 6000 points, and the running time is 60s. If you want to extend or shorten the running time, you only need to increase or decrease the length of the data accordingly.
[0074] In order to accurately reproduce the displacement of the free vibration test model, the present invention is different from the traditional mechanical drive device controlled by force. Instead, the displacement is set to the simulated target value by establishing a feedback system. The present invention measures the model displacement in real time, determines the motor output based on the error value between the real-time displacement and the target displacement, and thus changes the forcing force in real time so that the model displacement accurately reproduces the target displacement. See the specific process for details. Figure 7 , including the following steps:
[0075] (1) The system is placed in the flow field, and the free vibration test device and the mechanical drive test device are operated;
[0076] (2) The target value of the motion time history of the bridge segment model in the free vibration test device is denoted as A d , is the manually set target value; the motion time here is the displacement vector in three-dimensional space;
[0077] (3) At time i, measure the motion time history A(t i );
[0078] (4)A(t i ) and A d (t i ) has an error of E;
[0079] E=A(t i )-A d (t i )
[0080] (5) According to the positive or negative value of E, determine whether the motor output should be increased or decreased to accelerate or decelerate the model. If E < 0, it means that the actual displacement of the model is less than the target value, and the motor output should be increased; if E > 0, it means that the actual displacement of the model is greater than the target value, and the motor output should be reduced; if E = 0, the motor output remains unchanged;
[0081] (6) The motor outputs a forced force acting on the bridge segment model, and the motion state of the model changes;
[0082] (7) Determine whether all target schedules have been achieved. If not, set i = i + 1 and repeat from step 3;
[0083] (8) Finally, the displacement of the bridge segment model is made the same as the target displacement.
[0084] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.
Claims
1. A vibration simulation feedback method for reproducing displacement, characterized in that: The following steps are involved: (1) placing a free vibration test device and a mechanical drive test device in a flow field, and operating the free vibration test device and the mechanical drive test device; (2) The target motion time of the first bridge segment model in the free vibration test device is recorded as A d ; (3) At time i, measure the motion time history A(t i ); (4) Calculate A(t i ) and A d (t i ) has an error of E; (5) Determine whether to increase or decrease the motor output based on the positive or negative value of E; If E<0, increase the motor output; if E>0, reduce the motor output; if E=0, keep the motor output unchanged; (6) The motor outputs a forced force acting on the second bridge segment model in the mechanical drive test device, and the motion state of the model changes; (7) Determine whether all target schedules have been achieved. If not, set i = i + 1 and repeat from step (3); (8) Finally, the displacement of the second bridge segment model in the mechanical drive test device is made the same as the target value of the motion time course.
2. The method according to claim 1, characterized in that include: The free vibration test device comprises a first bridge segment model and an elastic suspension system, wherein the first bridge segment model is mounted on the elastic suspension system; The mechanical drive test device includes a second bridge segment model, a vertical motor motion track, a lateral motor motion track, and a torsion motor motion track; the second bridge segment model is connected and fixed to the torsion motor motion track.
3. The method according to claim 2, characterized in that The elastic suspension system is assembled from eight identical springs, wherein two of the springs are connected in series to form four identical spring strings and are suspended, and each spring string has the same height; Every two of the spring strings form a pair of spring strings, the two pairs of spring strings are symmetrically placed on both sides of the first bridge segment model, and the middle of each pair of spring strings is connected by a first connecting shaft; The middle parts of the two first connecting shafts are connected by a second connecting shaft, and the first bridge segment model is connected and fixed at the middle position on the second connecting shaft.
4. The method according to claim 2 or 3, characterized in that: The mechanical drive test device further includes three groups of motors, which are vertical motion motors, lateral motion motors and torsional motion motors, respectively controlling the motion of three degrees of freedom; wherein, The vertical motion motor is installed on the vertical motor motion track, the lateral motion motor is installed on the lateral motor motion track, and the torsion motion motor is installed on the torsion motor motion track.
5. The method according to claim 4, characterized in that The mechanical drive test device includes a base and brackets fixedly installed on both sides of the base, and a first slider installed on the brackets along the horizontal direction, a second slider installed on the first slider along the vertical direction, and the second bridge segment model installed rotationally between the second sliders are installed between the brackets. The second bridge segment model vibrates in one or more of the three degrees of freedom of horizontal, vertical and rotational directions.
6. The method according to claim 5, characterized in that The bracket is provided with the horizontal motor motion track in the horizontal direction, the first slider is slidably installed on the horizontal motor motion track, the first slider is provided with the vertical motor motion track in the vertical direction, and the second slider is slidably installed on the vertical motor motion track.
7. The method according to claim 6, characterized in that The bracket is provided with the lateral motion motor for driving the first slider to slide in the horizontal direction and the vertical motion motor for driving the second slider to slide in the vertical direction, and the second slider is provided with the torsional motion motor for driving the second bridge segment model to rotate.
8. The method according to claim 5, characterized in that The rotation axis of the second bridge segment model is arranged perpendicularly to the horizontal direction and the vertical direction respectively.
9. The method according to claim 5, characterized in that A plurality of feedback encoders are fixedly mounted on the bracket for real-time feedback of the output displacement time course.
10. The method according to claim 5, characterized in that The vibration form of the second bridge segment model at each degree of freedom is any one of the following motions: single-frequency simple harmonic motion, simple harmonic motion with multiple frequencies superimposed, motion with frequency varying with time, motion with amplitude varying with time, motion with mean varying with time, and random motion.
Citation Information
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