A low-frequency nonlinear damping calculation method for engineering structures based on a generalized van der pol oscillator model

Abstract

The application discloses a nonlinear structural damping calculation method based on a generalized Van der Pol oscillator model, and comprises the following steps: firstly, a segment model free vibration wind tunnel test under static wind condition is carried out, and a torsional displacement response time history of the segment model is collected; secondly, a test amplitude of each vibration period is picked up from the displacement response time history, and an instantaneous structural damping corresponding to each test amplitude is calculated; finally, a relationship between a nonlinear structural damping ratio and a time history is fitted by using the instantaneous structural damping and the corresponding test amplitude, and an expression of the nonlinear structural damping ratio is obtained. The significant effect of the application is that the nonlinear structural damping can be quickly and accurately calculated through the structural free vibration decay response time history, so as to provide a reliable basis for vibration response calculation and design work of large engineering structures.

Description

Technical Field

[0001] This invention relates to the field of nonlinear structural damping identification in engineering structures, and more specifically to a nonlinear structural damping calculation method based on the generalized van der Bohr oscillator model. Background Technology

[0002] Large-scale engineering structures (such as long-span bridges and tall buildings) experience complex and difficult-to-determine energy loss mechanisms under external dynamic loads due to uncertainties in factors such as internal material losses and component friction. Currently, there is no unified deterministic theory to describe structural damping. For bluff body sections prone to nonlinear vibrations, structural damping has a significant impact on structural response. Accurate understanding of the nonlinearity of structural damping is crucial for precise evaluation and prediction of the nonlinear vibration characteristics and response of engineering structural sections. Existing structural damping calculation methods exhibit significant errors in the small-amplitude phase of structural vibrations, resulting in noticeable fluctuations and unreliability. Therefore, it is necessary to develop calculation methods that can accurately identify nonlinear structural damping, improve the calculation of vibration response of large-scale engineering structures, and provide a reliable design basis for the design of such structures. Summary of the Invention

[0003] This invention provides a method for quickly and accurately calculating the nonlinear structural damping. The main technical solution adopted is carried out in the following steps:

[0004] Step 1: Conduct wind tunnel tests on the free vibration of the segmental model under still wind conditions. Apply an initial torsional excitation to the horizontally suspended engineering structure segmental model and collect the displacement response time history q of the segmental model in the torsional direction using a laser displacement meter.

[0005] Step 2: Extract the test amplitude A for each vibration cycle from the displacement response time history q. q,j Calculate the amplitude A for each test. q,j The corresponding instantaneous structural damping ξ s，j ;

[0006] Step 3: Using several instantaneous structural damping ξ s，j and the corresponding test amplitude A q,j Fitting the damping ratio ξ of the nonlinear structure s By relating it to time history q, we can obtain the formula for the damping ratio of the nonlinear structure. Attached Figure Description

[0007] Figure 1 The decay time history curves of torsional free vibration in a wind tunnel experiment of a segmental model under calm conditions;

[0008] Figure 2 For instantaneous structural damping ξ s，j With test amplitude A q,jDistribution diagram and the nonlinear structural damping ratio ξ obtained by fitting. s The curve showing the relationship between time history q;

[0009] Figure 3 To fit the response time history and compare the response time history obtained from wind tunnel tests. Detailed Implementation

[0010] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0011] A nonlinear structural damping calculation method based on the generalized van der Bohr oscillator model is performed according to the following steps:

[0012] Step 1: Conduct wind tunnel tests on the free vibration of the segmental model under still wind conditions. Apply an initial torsional excitation to the horizontally suspended engineering structure segmental model and collect the displacement response time history q of the segmental model in the torsional direction using a laser displacement meter.

[0013] The time history q curve of the specific segmental model free vibration wind tunnel test is as follows: Figure 1 As shown, from Figure 1 It can be seen that the time history q of the reciprocating vibration of the segmental model gradually decreases with time;

[0014] Step 2: Extract the test amplitude A for each vibration cycle from the displacement response time history q. q,j ,like Figure 1 As shown by the red dot;

[0015] Assuming the damping between two adjacent amplitudes remains constant during the vibration of the segmental model, the damping of the segmental model at each test amplitude A is calculated according to the following formula ①. q,j The corresponding instantaneous structural damping ξ s，j ;

[0016]

[0017] In the above formula:

[0018] A q,j The amplitude corresponding to the j-th oscillation period;

[0019] A q,j+1 This represents the amplitude corresponding to the (j+1)th oscillation period;

[0020] j = 1, 2, 3, ..., N; N is the extracted test amplitude A. q,j The total number;

[0021] according to Figure 1 Extracted test amplitude A q,j The calculated instantaneous structural damping ξ s，j like Figure 2 As shown, from Figure 2It can be seen that the distribution of instantaneous structural damping with test amplitude has a large degree of dispersion, which is more obvious when the amplitude is large;

[0022] Step 3: Several instantaneous structural damping ξ s，j and the corresponding test amplitude A q,j A set of fitted data is formed, and based on the set of fitted data, the damping ratio ξ of the nonlinear structure is fitted. s The relationship with time history q yields the formula for the damping ratio of the nonlinear structure;

[0023] A kind of ξ s The specific fitting relationship with q can be determined according to the following formula ②:

[0024] ξ s =-ρB 2 / m eq *K a,eq , formula②;

[0025] in:

[0026] ρ is the air density;

[0027] B represents the feature size of the segment model;

[0028] m eq For structural equivalent mass;

[0029]

[0030] K a0 ε and β are parameters of the aeroelastic effect;

[0031] Γ(·) is the gamma function;

[0032] m eq = m / L;

[0033] m represents the mass of the segmental model system;

[0034] L is the structural feature length;

[0035] Substituting the fitted data set into formula ② yields the aeroelastic effect-related parameter K. a0 , ε, β.

[0036] according to Figure 2 The parameters K obtained from the fitting results a0 =0.000441, ε = -1.23, β = 1.28; combined with other relevant parameters, the visual expression of the fitted formula ② is as follows: Figure 2 As shown by the red curve in the image.

[0037] Step 4: Calculate the fitted response time history q(t) of the structure's free vibration decay using the following formula ③;

[0038]

[0039] in:

[0040] A q (t) represents the instantaneous vibration amplitude in response to q;

[0041] t represents time;

[0042] ψ represents the phase of the vibration time history;

[0043] ω q Let q be the natural circular frequency of the response q of the freely vibrating system;

[0044] Plot the calculation results from step four and the wind tunnel test structure from step one in the same coordinate system; the results are as follows: Figure 3 As shown; from Figure 3 It can be seen that the fitted response time-time curve highly coincides with the response time-time curve obtained from the wind tunnel test; therefore, it can be concluded that the nonlinear structural damping ratio ξ calculated using the above method is accurate. s It can accurately predict / calculate a fitted response time history that is highly similar to the experimental response time history.

[0045] Beneficial effects: The significant advantage of this invention is that it enables the rapid and accurate calculation of nonlinear structural damping through the time history of the attenuation response of free vibration of a structure, thereby providing a reliable basis for the calculation and design of vibration response of large-scale engineering structures.

[0046] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention. Those skilled in the art, under the guidance of the present invention, can make various similar representations without departing from the spirit and claims of the present invention, and such modifications all fall within the protection scope of the present invention.

Claims

1. A nonlinear structural damping calculation method based on the generalized van der Bohr oscillator model, characterized in that... Follow these steps: Step 1: Conduct wind tunnel tests on the free vibration of the segmental model under still wind conditions. Apply an initial torsional excitation to the horizontally suspended engineering structure segmental model, and collect the displacement response time history of the segmental model in the torsional direction using a laser displacement meter. q ; Step 2: From the displacement response time history q Extract the test amplitude for each vibration cycle. Aq,j Calculate the amplitude of each test. Aq,j Corresponding instantaneous structural damping ξ s，j ; Step 3: Using several instantaneous structural damping ξ s，j and the corresponding test amplitude Aq,j Fitting the damping ratio of nonlinear structures ξ s With time schedule q Based on the relationship, the formula for the damping ratio of the nonlinear structure is obtained; In step two, assuming that the damping between two adjacent amplitudes remains constant during the vibration of the segmental model, the instantaneous structural damping of the segmental model is calculated according to the following formula ①. ξ s，j ; Formula ①; In the above formula: Aq, j For the first j The test amplitude corresponding to each vibration cycle; Aq, j +1 is the first j+ The test amplitude corresponding to one vibration cycle; In step three, the damping ratio of the nonlinear structure is fitted according to the following formula ②. ξ s With time schedule q Relationship; ξ s = ρB 2 / m eq * K a,eq , formula ②; in: ρ air density; B The feature size of the segment model; m eq For structural equivalent mass; ； K a0 , ε , β These are parameters related to the aeroelastic effect. Γ (·) is the gamma function.

2. The nonlinear structural damping calculation method based on the generalized van der Bohr oscillator model according to claim 1, characterized in that: In formula ②, m eq = m / L ; in: m For the quality of the segmental model system; L The length is the structural feature length.

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