Method for extracting bridge nonlinear structure damping based on free vibration test

Abstract

The invention discloses a method for extracting bridge nonlinear structure damping based on a free vibration test, relates to the technical field of bridge wind resistance, solves the stability problem of a bridge under the action of wind, and provides support for optimizing bridge design and improving bridge safety. The method comprises the following steps: S1, carrying out a bridge segment test in a wind tunnel to obtain test structure damping and test total damping, and calculating test aerodynamic damping to obtain real bridge aerodynamic damping; s2, acquiring a time-varying amplitude curve of the bridge from static to vortex-induced vibration under a natural wind condition, and processing the time-varying amplitude curve to obtain the total damping of the real bridge; s3, real bridge structural damping is calculated through the real bridge pneumatic damping and the real bridge total damping; the stability problem of the bridge under the wind effect is solved, and support is provided for optimizing the bridge design and improving the bridge safety.

Description

Technical Field

[0001] This invention relates to the field of bridge wind resistance technology, specifically to a method for extracting the nonlinear structural damping of bridges based on free vibration tests. Background Technology

[0002] Structural damping of a bridge is a crucial characteristic of energy dissipation during vibration. It reflects energy loss caused by internal friction of bridge materials, friction at joints, and inelastic behavior of the structure. Structural damping plays a vital role in bridge design, analysis, and operation. It not only controls the bridge's vibration response and improves wind and seismic resistance but also assesses the bridge's health and optimizes its design. Proper design and management of structural damping ensures the safety, comfort, and economy of bridges, supporting the sustainable development of bridge engineering. Therefore, real-time monitoring of changes in bridge structural damping is essential for ensuring traffic safety and optimizing bridge structures. Testing bridge structural damping typically involves forced vibration; however, this method requires a vibrator to induce resonance in an existing bridge, which is practically difficult and costly.

[0003] Free vibration testing is one of the fundamental methods in structural dynamics research. As early as the beginning of the 20th century, scientists and engineers began using free vibration tests to study the dynamic characteristics of structures, such as natural frequencies, damping ratios, and mode shapes. With the development of bridges, high-rise buildings, and long-span structures, free vibration testing has gradually become an important means of evaluating the dynamic performance of these structures. With the increase in long-span bridges and high-rise buildings, wind-induced vibration problems (such as flutter and vortex-induced vibration) have become increasingly prominent. Free vibration testing has become an important tool for studying the dynamic response of structures under wind loads. Through free vibration testing, the aerodynamic damping of the structure can be extracted, providing a basis for wind-resistant design. As a classic and effective experimental method, free vibration testing has wide applications in structural dynamics, wind engineering, and health monitoring. It can directly measure the dynamic characteristics of structures, providing important basis for wind-resistant design, numerical model verification, health monitoring, and code formulation. With technological advancements, the role of free vibration testing in engineering practice will become even more prominent. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method for extracting the nonlinear structural damping of bridges based on free vibration tests, which solves the stability problem of bridges under wind action and provides technical support for optimizing bridge design and improving bridge safety.

[0005] A method for extracting the nonlinear structural damping of bridges based on free vibration tests includes:

[0006] S1. Conduct bridge segment tests in a wind tunnel to obtain the test structure damping and the total test damping, calculate the test aerodynamic damping, and then obtain the actual bridge aerodynamic damping.

[0007] S2. Collect the time-varying amplitude curves of the bridge from rest to vortex-induced vibration under natural wind conditions and process them to obtain the total damping of the actual bridge.

[0008] S1 and S2 have no specific order;

[0009] S3. Calculate the structural damping of the actual bridge using the aerodynamic damping and total damping of the actual bridge.

[0010] Further, S1 includes:

[0011] S11. The damping of the test structure was obtained by the free vibration attenuation method under windless conditions;

[0012] S12. The total damping of the test is obtained by the time-varying amplitude curve of the vortex-induced vibration of the bridge under windy conditions.

[0013] S13. The test aerodynamic damping is obtained by using the total test damping and the test structural damping as the actual bridge aerodynamic damping.

[0014] Further, S2 includes:

[0015] S21. The actual bridge begins to vibrate under natural wind conditions;

[0016] S22. Collect the time-varying amplitude curve of the actual bridge from rest to vortex-induced vibration;

[0017] S23. Obtain the total damping of the real bridge through Hilbert transformation.

[0018] Further, S11 includes: applying an initial excitation to the bridge model to induce free vibration, and analyzing the damping ξ of the test structure by recording the vibration decay process. s Specifically: For a single-degree-of-freedom system, the displacement response of free vibration can be expressed as:

[0019]

[0020] in:

[0021] x(t) is the displacement at time t;

[0022] X0 is the initial amplitude;

[0023] ξ is the damping ratio;

[0024] ω n It is the system's natural frequency (undamped natural frequency);

[0025] ω dIt is the damped natural frequency.

[0026] φ is the phase angle;

[0027] The damping ratio can be calculated using the logarithmic decay method by measuring the amplitude of vibration decay. Assuming that the amplitudes of two adjacent peaks are X1 and X2, the damping ratio ξ can be calculated using the following formula:

[0028]

[0029] Wherein, δ is the logarithmic decay rate, defined as:

[0030] .

[0032] Further, S12 includes: recording the time-varying amplitude curve of a bridge segment from rest to vortex-induced vibration during vortex-induced vibration, and obtaining the total experimental damping ξ. h , specifically:

[0033] The time-varying amplitude of the nonlinear vibration process is identified based on the Hilbert Transform (HT) method, and the total damping of the experiment is solved based on this.

[0034] For a certain nonlinear vibration time history signal y(t), its Hilbert transform is:

[0035]

[0036] From this we can obtain

[0037]

[0038] in:

[0039] y(t) is a nonlinear vibration signal.

[0040] A(t) is the time-varying amplitude of the nonlinear vibration signal y(t);

[0041] The time-varying phase of the nonlinear vibration signal y(t) corresponds to the instantaneous value at each time step.

[0042]

[0043] Meanwhile, the time-varying frequency of the nonlinear vibration signal can be obtained using the HT transform:

[0044]

[0045] Using the time-varying amplitude, phase, and frequency information of the nonlinear vibration signal obtained by Hilbert transform (HT), since the time-varying amplitude obtained directly through HT is a discrete signal, it needs to be fitted into an analytical equation form for convenient differentiation and calculation of modal damping. This paper proposes to use the Gompertz model to fit the time-varying amplitude curve of the nonlinear vibration signal. The model expression is as follows:

[0046]

[0047] in:

[0048] A hm Indicates the steady-state response amplitude;

[0049] a0 and a1 are constants;

[0050] t c This indicates the moment when the logarithmic amplitude envelope reaches its inflection point.

[0051] After obtaining the time-varying amplitude curve, the time-varying modal total damping can be solved by the following formula:

[0052]

[0053] Furthermore, the total damping that varies with amplitude can be obtained as follows:

[0054] .

[0056] Further, S13 includes: determining the test aerodynamic damping using the total test damping and the test structural damping as the actual bridge aerodynamic damping; specifically:

[0057] ξ a =ξ h -ξ s

[0058] ξ a For aerodynamic damping;

[0059] ξ h Total damping;

[0060] ξ s For structural damping.

[0061] The beneficial effects of this invention include:

[0062] To address the difficulty in extracting aerodynamic damping from actual bridges using existing technologies, this invention first conducts free vibration tests on bridge segments in a wind tunnel. Under windless conditions, the decay rate of the vibration amplitude over time is analyzed, and the decay process of the model vibration is recorded. The structural damping of the test system is obtained by analyzing the decay rate of the vibration amplitude over time. Then, by acquiring the time-varying amplitude curves of the bridge segments undergoing vortex-induced vibration in the wind tunnel test, the total damping value of the bridge segments during vortex-induced vibration is obtained. Since the total damping in a nonlinear vibration process is the sum of structural damping and aerodynamic damping, and vortex-induced vibration is a single-degree-of-freedom nonlinear vibration, the aerodynamic damping can be obtained by subtracting the structural damping from the total damping collected and analyzed when the bridge undergoes vortex-induced vibration. Therefore, subtracting the structural damping of the test system from the total damping obtained from the wind tunnel test yields the aerodynamic damping of the bridge segments during vortex-induced vibration in the test. Since the aerodynamic damping of the main beam of the bridge is only related to its aerodynamic shape, the aerodynamic damping obtained through the segment model test is approximately equal to the aerodynamic damping in the actual bridge. Based on this characteristic, and when a bridge actually experiences vortex-induced vibration, the total damping of the actual bridge can be obtained by analyzing the time-varying amplitude curve using the same method as in previous wind tunnel tests. Subtracting the aerodynamic damping obtained through segmental model tests from the total actual bridge damping yields the actual bridge structural damping, thus extracting the nonlinear structural damping of the actual bridge. This provides crucial scientific evidence for bridge wind-resistant design, vibration control, health monitoring, and code formulation, addressing the stability issues of bridges under wind loads and supporting the optimization of bridge design and improvement of bridge safety. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating a method for extracting the nonlinear structural damping of a bridge based on free vibration tests, as described in an embodiment of this application.

[0064] Figure 2 This is a schematic diagram illustrating an implementation example of a wind tunnel test segment involved in the embodiments of this application;

[0065] Figure 3 This is a schematic diagram of the damping curve involved in an embodiment of this application; wherein, Figure 3 (a) is a schematic diagram of the aerodynamic damping curve of the actual bridge obtained from the wind tunnel segment test; Figure 3 (b) is a schematic diagram of the total damping curve of the actual bridge obtained under natural wind conditions; Figure 3 (c) is a schematic diagram of the calculated damping of the actual bridge structure. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0067] Example 1

[0068] The following is in conjunction with the appendix Figures 1-2 Specific embodiments of the present invention will be described in detail;

[0069] A method for extracting the nonlinear structural damping of bridges based on free vibration tests, such as Figure 1 As shown, it includes:

[0070] S1. Conduct bridge segment tests in a wind tunnel, such as... Figure 2 As shown, the test structure damping and total test damping are obtained, the test aerodynamic damping is calculated, and then the actual bridge aerodynamic damping is obtained.

[0071] S11. Under windless conditions, the damping of the test structure is obtained by the free vibration attenuation method. An initial excitation is applied to the bridge model to make it start free vibration. The damping of the test structure is obtained by recording the vibration attenuation process.

[0072] S12. Under windy conditions, obtain the total test damping by recording the time-varying amplitude curve of the bridge's vortex-induced vibration; when the bridge segment is under vortex-induced vibration, record its time-varying amplitude curve from rest to vortex-induced vibration to obtain the total test damping.

[0073] S13. The test aerodynamic damping is obtained by using the total test damping and the test structural damping as the actual bridge aerodynamic damping.

[0074] S2. Collect the time-varying amplitude curves of the bridge from rest to vortex-induced vibration under natural wind conditions and process them to obtain the total damping of the actual bridge.

[0075] S21. The actual bridge begins to vibrate under natural wind conditions;

[0076] S22. Collect the time-varying amplitude curve of the actual bridge from rest to vortex-induced vibration;

[0077] S23. Obtain the total damping of the real bridge through Hilbert transformation.

[0078] S3. Calculate the structural damping of the actual bridge using the aerodynamic damping and total damping of the actual bridge.

[0079] Specifically, in step S11, the principle of obtaining the damping of the test structure through the free vibration attenuation method is as follows:

[0080] For a single-degree-of-freedom system, the displacement response of free vibration can be expressed as:

[0081]

[0082] x(t) is the displacement at time t;

[0083] X0 is the initial amplitude;

[0084] ξ is the damping ratio;

[0085] ω n It is the system's natural frequency (undamped natural frequency);

[0086] ω d It is the damped natural frequency.

[0087] φ is the phase angle.

[0088] The damping ratio can be calculated using the logarithmic decay method by measuring the amplitude of vibration decay. Assuming two adjacent peak amplitudes are X1 and X2, the damping ratio ξ can be calculated using the following formula:

[0089]

[0090] Wherein, δ is the logarithmic decay rate, defined as:

[0091]

[0092] Step S12 identifies the time-varying amplitude of the nonlinear vibration process based on the Hilbert transform method, and solves for the total experimental damping based on this. For a certain nonlinear vibration time history signal y(t), its Hilbert transform is:

[0093]

[0094] in:

[0095] y(t) is a nonlinear vibration signal.

[0096] Y(t) is an analytic signal.

[0097] A(t) is the time-varying amplitude of the nonlinear vibration signal y(t).

[0098] y(t) is the time-varying phase of the nonlinear vibration signal, which corresponds to the instantaneous value at each time step.

[0099]

[0100] Meanwhile, the time-varying frequency of the nonlinear vibration signal can be obtained using the Hilbert transform:

[0101]

[0102] Using the time-varying amplitude, phase, and frequency information of the nonlinear vibration signal obtained by Hilbert transform (HT), since the time-varying amplitude obtained directly through HT is a discrete signal, it needs to be fitted into an analytical equation form for convenient differentiation and calculation of modal damping. This paper proposes using the Gompertz model to fit the time-varying amplitude curve of the nonlinear vibration signal. The model expression is as follows:

[0103]

[0104] in:

[0105] A hm Indicates the steady-state response amplitude;

[0106] a0 and a1 are constants;

[0107] t c This indicates the moment when the logarithmic amplitude envelope reaches its inflection point.

[0108] After obtaining the time-varying amplitude curve, the time-varying modal total damping can be solved by the following formula:

[0109]

[0110] Furthermore, the total damping that varies with amplitude can be obtained as follows:

[0111]

[0112] In step S13, the formula for calculating the experimental aerodynamic damping is as follows:

[0113] ξ a =ξ h -ξ s

[0114] ξ a For aerodynamic damping;

[0115] ξ h Total damping;

[0116] ξ s For structural damping.

[0117] The principle of obtaining the total damping of the real bridge through the Hilbert transformation in S23 is the same as that in S12.

[0118] S1 and S2 have no specific order;

[0119] In step S3, the formula for calculating the damping of the actual bridge structure is as follows:

[0120] ξ s =ξ h -ξ a

[0121] ξ a For aerodynamic damping;

[0122] ξ h Total damping;

[0123] ξ s For structural damping.

[0124] The specific damping calculation results are as follows: Figure 3 As shown, Figure 3 (a) is a schematic diagram of the aerodynamic damping curve of the actual bridge obtained from the wind tunnel segment test; Figure 3 (b) is a schematic diagram of the total damping curve of the actual bridge obtained under natural wind conditions; Figure 3 (c) is a schematic diagram of the calculated damping of the actual bridge structure. The diagram mainly compares the original cross section with other working conditions. The other working conditions are the cross section after the addition of diversion measures. It can be seen that the damping calculation results are different for different cross sections.

[0125] The embodiments described above merely illustrate specific implementation methods of this application, and while the descriptions are detailed and specific, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the technical solution of this application, and these modifications and improvements all fall within the scope of protection of this application.

Claims

1. A method for extracting the nonlinear structural damping of bridges based on free vibration tests, characterized in that, include: S1. Conduct bridge segment tests in a wind tunnel to obtain the test structure damping and the total test damping, calculate the test aerodynamic damping, and then obtain the actual bridge aerodynamic damping. S2. Collect the time-varying amplitude curves of the bridge from rest to vortex-induced vibration under natural wind conditions and process them to obtain the total damping of the actual bridge. S1 and S2 have no specific order; S3. Calculate the structural damping of the actual bridge using the aerodynamic damping and total damping of the actual bridge.

2. The method for extracting the nonlinear structural damping of a bridge based on free vibration tests according to claim 1, characterized in that, S1 includes: S11. The damping of the test structure was obtained by the free vibration attenuation method under windless conditions; S12. The total damping of the test is obtained by the time-varying amplitude curve of the vortex-induced vibration of the bridge under windy conditions. S13. The test aerodynamic damping is obtained by using the total test damping and the test structural damping as the actual bridge aerodynamic damping.

3. The method for extracting the nonlinear structural damping of a bridge based on free vibration tests according to claim 1, characterized in that, S2 includes: S21. The actual bridge begins to vibrate under natural wind conditions; S22. Collect the time-varying amplitude curve of the actual bridge from rest to vortex-induced vibration; S23. Obtain the total damping of the real bridge through Hilbert transformation.

4. The method for extracting the nonlinear structural damping of a bridge based on free vibration tests according to claim 2, characterized in that, S11 includes: applying an initial excitation to the bridge model to induce free vibration, and analyzing the damping ξ of the test structure by recording the vibration decay process. s Specifically: For a single-degree-of-freedom system, the displacement response of free vibration can be expressed as: Where: x(t) is the displacement at time t; X0 is the initial amplitude; ξ is the damping ratio; ω n It is the system's natural frequency (undamped natural frequency); ω d It is the damped natural frequency. φ is the phase angle; The damping ratio can be calculated using the logarithmic decay method by measuring the amplitude of vibration decay. Assuming that the amplitudes of two adjacent peaks are X1 and X2, the damping ratio ξ can be calculated using the following formula: Wherein, δ is the logarithmic decay rate, defined as:

5. The method for extracting the nonlinear structural damping of a bridge based on free vibration tests according to claim 2, characterized in that, S12 includes: recording the time-varying amplitude curve of a bridge segment from rest to vortex-induced vibration during vortex-induced vibration, and obtaining the total experimental damping ξ. h Specifically: for a certain nonlinear vibration time history signal y(t), its Hilbert transform is: From this we can obtain in: y(t) is the nonlinear vibration signal; A(t) is the time-varying amplitude of the nonlinear vibration signal y(t); θ(t) is the time-varying phase of the nonlinear vibration signal y(t), that is, the instantaneous value corresponding to each time step; Meanwhile, the time-varying frequency of the nonlinear vibration signal can be obtained using the HT transform: The time-varying amplitude curve of the nonlinear vibration signal is fitted using the Gompertz model, and the model expression is as follows: in: A hm The steady-state response amplitude is represented by a0 and a1, which are constants; t c This indicates the moment when the logarithmic amplitude envelope reaches its inflection point; after obtaining the time-varying amplitude curve, the time-varying modal total damping can be solved using the following formula: Furthermore, the total damping that varies with amplitude can be obtained as follows:

6. The method for extracting the nonlinear structural damping of a bridge based on free vibration tests according to claim 2, characterized in that, S13 includes: determining the test aerodynamic damping using the total test damping and the test structural damping as the actual bridge aerodynamic damping; specifically: x a =ξ h -x s ξ a For aerodynamic damping; ξ h For total damping; ξ s For structural damping.

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