Parameter design method and system of nonlinear viscous inertial damper

Abstract

The application belongs to the technical field of vibration control, and discloses a parameter design method and system of a nonlinear viscous inertial damper. The parameter design method comprises the following steps: continuously adjusting a velocity index α in a nonlinear damping force formula, calculating a low-order modal damping ratio after the velocity index α is adjusted by using a free vibration decay method, and obtaining a preselected range of the velocity index α that meets a preset design requirement; in the preselected range, obtaining a reduction rate δ of a high-order modal damping ratio corresponding to different velocity indexes α, obtaining a set of the reduction rates δ of the high-order modal damping ratio, and the velocity index δ corresponding to the minimum reduction rate δ in the set of the reduction rates δ that meets the preset requirement is the target velocity index. The damper designed by the nonlinear parameters can solve the deficiencies of linear design and improve the multi-modal vibration reduction control performance of a flexible structure.

Description

Technical Field

[0001] This invention belongs to the field of vibration control technology, and more specifically, relates to a parameter design method and system for a nonlinear viscous inertial mass damper. Background Technology

[0002] Currently, in engineering, dampers used for structural control are often designed using linear parameters during the parametric design phase. This greatly simplifies the design process and improves efficiency. However, linear parameter design cannot maximize damper performance, and in practical engineering, damper elements rarely exhibit ideal linearity. Therefore, nonlinear parameter design is a more practical and effective method. Taking the multimodal vibration control parameter design of cables as an example, as the span of cable-stayed bridges increases, the cables also become longer, with many exceeding 600 meters. Linear parameter design cannot meet the requirements of multimodal control at this point, and linear dampers struggle to provide effective control over a wide range of vibration modes in ultra-long cables. Therefore, finding a nonlinear parameter design method has significant practical implications and engineering needs. Summary of the Invention

[0003] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a parameter design method and system for nonlinear viscous inertial mass dampers. The damper designed with nonlinear parameters can overcome the shortcomings of linear design and improve the multimodal vibration reduction and control performance of flexible structures.

[0004] To achieve the above objectives, according to one aspect of the present invention, a parameter design method for a nonlinear viscous inertial mass damper is provided. The nonlinear viscous inertial mass damper includes a nonlinear damper and an inertial mass unit, wherein the nonlinear damper and the inertial mass unit are connected in parallel. The parameter design method includes: S1: continuously adjusting the velocity exponent α in the nonlinear damping force formula, wherein the nonlinear damping force formula f is;

[0005] f = cv α

[0006] Where c is the damping coefficient of the nonlinear damper, and v is the velocity at the end of the damper;

[0007] S2: The low-order modal damping ratio after adjusting the velocity index α is calculated using the free vibration decay method to obtain the pre-selected range of the velocity index α that meets the preset design requirements;

[0008] S3: Within the preselected range, obtain the reduction rate δ of the higher-order modal damping ratio corresponding to different velocity indices α, obtain the set of reduction rates δ of the higher-order modal damping ratio, and the velocity index δ corresponding to the minimum reduction rate in the set of reduction rates δ of the higher-order modal damping ratio that meets the preset requirements is the target velocity index.

[0009] Preferably, in step S3, the reduction rate δ of the higher-order modal damping ratio corresponding to different velocity indices α is obtained, specifically using the following formula to obtain the reduction rate δ of the higher-order modal damping ratio:

[0010]

[0011] in, g(α) is the gamma function. U is the nth natural frequency of the cable when no damper is installed. xa The vibration amplitude at the damper installation location. c is the damping coefficient of the nonlinear damper, T is the axial tensile force of the test object, and xa is the installation position of the damper.

[0012] Preferably, in step S1, the damping coefficient c of the nonlinear damper is obtained using the following formula:

[0013]

[0014] Where n represents the first n modes, L represents the effective length of the test object, m represents the mass per unit length of the test object, T represents the axial tensile force of the test object, and xa represents the installation position of the damper.

[0015] Preferably, before step S1, the theoretical modal damping ratio of the nonlinear viscous inertial mass damper is obtained. If the low-order modal damping in the theoretical modal damping ratio does not meet the preset design requirements, then step S1 is executed.

[0016] Preferably, the theoretical modal damping ratio ξ is calculated using the following formula:

[0017]

[0018] Where ω is the vibration frequency and c is the damping coefficient of the nonlinear damper. n represents the first n modes, L represents the effective length of the test object, m represents the mass per unit length of the test object, xa represents the installation position of the damper, and T represents the axial tensile force of the test object.

[0019] A second aspect of this application provides a parameter design system for a nonlinear viscous inertial mass damper, the nonlinear viscous inertial mass damper comprising a nonlinear damper and an inertial mass unit, wherein the nonlinear damper and the inertial mass unit are connected in parallel, and the parameter design system comprises:

[0020] Adjustment module: Used to continuously adjust the velocity exponent α in the nonlinear damping force formula, where the nonlinear damping force formula f is;

[0021] f = cv α

[0022] Where c is the damping coefficient of the nonlinear damper, and v is the velocity at the end of the damper;

[0023] Calculation module: used to calculate the low-order modal damping ratio after adjusting the velocity index α using the free vibration decay method, and to obtain the pre-selected range of velocity index α that meets the preset design requirements;

[0024] Acquisition module: Used to acquire the reduction rate δ of higher-order modal damping ratios corresponding to different velocity indices α within the preselected range, obtain the set of reduction rates δ of higher-order modal damping ratios, and the velocity index δ corresponding to the minimum reduction rate in the set of reduction rates δ of higher-order modal damping ratios that meets the preset requirements is the target velocity index.

[0025] Preferably, the module obtains the reduction rate δ of the higher-order modal damping ratio corresponding to different velocity indices α, specifically using the following formula to obtain the reduction rate δ of the higher-order modal damping ratio:

[0026]

[0027] in, g(α) is the gamma function. U is the nth natural frequency of the cable when no damper is installed. xa η represents the vibration amplitude at the damper installation location. n for c is the damping coefficient of the nonlinear damper, T is the axial tensile force of the test object, and xa is the installation position of the damper.

[0028] In summary, compared with the prior art, the parameter design method and system for a nonlinear viscous inertial mass damper provided by this invention have the following advantages:

[0029] 1. Compared with the traditional linear parameter design method, the nonlinear parameter design method proposed in this invention is more in line with the needs of actual engineering, and after design, the viscous inertial mass damper can achieve better control performance.

[0030] 2. This application obtains a pre-selected range of damping ratios for low-order modes by continuously adjusting the velocity index, and then further selects a velocity index that satisfies the damping ratio for high-order modes by combining the reduction rate within the pre-selected range. The designed parameters can simultaneously meet the requirements of low-order modes for wind and rain vibration control and high-order modes for vortex-induced vibration control.

[0031] 3. In this nonlinear damper, the damping coefficient c is designed nonlinearly based on the determined linear parameters. The design combines numerical methods such as the free vibration attenuation method with theoretical methods such as the attenuation rate, making the overall design process clear and operable, and greatly reducing the workload of the designer. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the nonlinear viscous inertial mass damper of this application;

[0033] Figure 2 This is a step-by-step diagram of the parameter design method for the nonlinear viscous inertial mass damper of this application;

[0034] Figure 3 This is a schematic diagram of the damper of this application installed on the cable for cable vibration reduction;

[0035] Figure 4 This is an illustration of calculating the modal damping ratio using the free vibration attenuation method;

[0036] Figure 5A It is the modal damping ratio of the linearly designed viscous inertial mass damper on the cable;

[0037] Figure 5B It is the modal damping ratio of the viscous inertial mass damper on the cable after nonlinear design. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0039] The present invention provides a parameter design method for a nonlinear viscous inertial mass damper, wherein the nonlinear viscous inertial mass damper includes a nonlinear damper and an inertial mass unit, such as... Figure 1 As shown, the nonlinear damper and the inertial mass unit are connected in parallel, as follows: Figure 2 As shown, the parameter design method includes the following steps S1 to S3. This application uses the multimodal vibration control of a cable as an example to illustrate the nonlinear parameter design method in detail, and the schematic diagram of the damper installed on the cable is shown below. Figure 3 As shown in Table 1 below, these are the specific parameters of the ultra-long cable in this application. We need to perform linear and nonlinear designs based on these parameters.

[0040]

[0041] Table 1

[0042] S1: Continuously adjust the velocity exponent α in the nonlinear damping force formula, where the nonlinear damping force formula f is;

[0043] f = cv α

[0044] Where c is the damping coefficient of the nonlinear damper, and v is the velocity at the end of the damper.

[0045] In a further preferred embodiment, the damping coefficient c of the nonlinear damper is:

[0046]

[0047] Where n represents the first n modes, L represents the effective length of the test object, m represents the mass per unit length of the test object, f represents the axial tensile force of the test object, and xa represents the installation position of the damper.

[0048] In a further preferred embodiment, step S1 is preceded by obtaining the theoretical modal damping ratio of the nonlinear viscous inertial mass damper. If the low-order modal damping in the theoretical modal damping ratio does not meet the preset design requirements, then step S1 is executed.

[0049] In a further preferred embodiment, the theoretical modal damping ratio ξ is calculated using the following formula:

[0050]

[0051] Where ω is the vibration frequency and c is the damping coefficient of the nonlinear damper. n represents the first n modes, L represents the effective length of the test object, m represents the mass per unit length of the test object, xa represents the installation position of the damper, and T represents the axial tensile force of the test object.

[0052] S2: The low-order modal damping ratio after adjusting the velocity index α is calculated using the free vibration decay method to obtain a pre-selected range of velocity index α that meets the preset design requirements. Subsequently, by continuously adjusting the velocity index α of the nonlinear damping and using the free vibration decay method to calculate the low-order modal damping ratio value after adjustment, the range of velocity index α that meets the low-order modal damping ratio design requirements is identified. A schematic diagram of the free vibration decay method can be seen... Figure 4 The dotted line represents the free vibration decay curve of the cable under additional damping. This application uses this curve to calculate the modal damping ratio.

[0053] S3: Within the preselected range, obtain the reduction rate δ of the higher-order modal damping ratio corresponding to different velocity indices α, obtain the set of reduction rates δ of the higher-order modal damping ratio, and the velocity index δ corresponding to the minimum reduction rate in the set of reduction rates δ of the higher-order modal damping ratio that meets the preset requirements is the target velocity index.

[0054] In a further optimized scheme, the reduction rate δ of the higher-order modal damping ratio corresponding to different velocity indices α is obtained. Specifically, the reduction rate δ of the higher-order modal damping ratio is obtained using the following formula:

[0055]

[0056] in, g(α) is the gamma function. U is the nth natural frequency of the cable when no damper is installed. xa η represents the vibration amplitude at the damper installation location. n for c is the damping coefficient of the nonlinear damper, T is the axial tensile force of the test object, and xa is the installation position of the damper.

[0057] The reduction ratio δ of the higher-order modal damping ratio can be obtained by the following steps:

[0058] S3.1 First, we introduce the following formula.

[0059]

[0060] S3.2 Calculate the theoretical modal damping ratio according to the formula in S3.1:

[0061]

[0062] Based on extensive numerical simulations and experimental data, we assume It is always less than 1, and its magnitude is on the order of 10. -1 ~10 -2 Therefore, Δ is always greater than 1 and very close to 1.

[0063] For items with significant impact Find the partial derivative:

[0064]

[0065] In other words, as the vibration order increases, the performance of nonlinear damping compared to linear damping continuously decreases. Therefore, we only need to look at the performance reduction rate δ of nonlinear damping in the highest-order control mode, which proves the rationality of the calculation of the damping ratio of the highest-order mode in this application.

[0066] Verification has shown that when the velocity index is around 1, for most high-order vibrations of cables, the performance loss of introducing nonlinear damping is at most 4.6% to 0.2% compared to linear damping.

[0067] A second aspect of this application provides a parameter design system for a nonlinear viscous inertial mass damper, the nonlinear viscous inertial mass damper comprising a nonlinear damper and an inertial mass unit, wherein the nonlinear damper and the inertial mass unit are connected in parallel, and the parameter design system comprises:

[0068] Adjustment module: Used to continuously adjust the velocity exponent α in the nonlinear damping force formula, where the nonlinear damping force formula f is;

[0069] f = cv α

[0070] Where c is the damping coefficient of the nonlinear damper, and v is the velocity at the end of the damper;

[0071] Calculation module: used to calculate the low-order modal damping ratio after adjusting the velocity index α using the free vibration decay method, and to obtain the pre-selected range of velocity index α that meets the preset design requirements;

[0072] Acquisition module: Used to acquire the reduction rate δ of higher-order modal damping ratios corresponding to different velocity indices α within the preselected range, obtain the set of reduction rates δ of higher-order modal damping ratios, and the velocity index δ corresponding to the minimum reduction rate in the set of reduction rates δ of higher-order modal damping ratios that meets the preset requirements is the target velocity index.

[0073] In a further preferred embodiment, the reduction rate δ of the higher-order modal damping ratio corresponding to different velocity indices α is obtained in the acquisition module. Specifically, the reduction rate δ of the higher-order modal damping ratio is obtained using the following formula:

[0074]

[0075] in, g(α) is the gamma function. U is the nth natural frequency of the cable when no damper is installed. xa η represents the vibration amplitude at the damper installation location. n for c is the damping coefficient of the nonlinear damper, T is the axial tensile force of the test object, and xa is the installation position of the damper.

[0076] Figure 5A and Figure 5B The image shows a comparison of the damping ratios of the first 76 modes of the ultra-long cable under viscous inertial mass dampers with linear and nonlinear designs. Figure 5A This is the case in linear design. Figure 5B This is the case when using nonlinear parameter design. As can be clearly seen from the two figures, after nonlinear design, the modal damping ratio provided by the damper can simultaneously meet the requirements of both low-order modes (solid line) and high-order modes (dashed line). In contrast, linear design can only meet the requirements of high-order modes and cannot take into account the design requirements of the most important low-order modes. Therefore, the nonlinear parameter design method proposed in this invention can effectively improve the control performance of the damper.

[0077] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for parameter design of a nonlinear viscous inertial damper, characterized by, The nonlinear viscous inertial mass damper includes a nonlinear damper and an inertial mass unit, wherein the nonlinear damper and the inertial mass unit are connected in parallel, and the parameter design method includes: S1: Continuously adjust the velocity exponent in the nonlinear damping force formula where the nonlinear damping force formula is; where c is the damping coefficient of the nonlinear damper, is the velocity of the damper end point; S2: Calculate the adjustment speed index by using the free vibration decay method the low-order modal damping ratio after the adjustment, and obtain the speed index satisfying the preset design requirement the preselected range; S3: Within the pre-selected range, obtain different speed indices. The corresponding reduction rate of higher-order modal damping ratio To obtain the reduction rate of the higher-order modal damping ratio Set, reduction rate of higher-order modal damping ratio The speed index corresponding to the minimum reduction rate that centrally meets the preset requirements This is the target speed index; In step S3, different speed indices are obtained. The corresponding reduction rate of higher-order modal damping ratio The reduction rate of the higher-order modal damping ratio is obtained using the following formula. : in, , For gamma function, Let n be the nth natural frequency of the cable when no damper is installed. The vibration amplitude at the damper installation location. for , c The damping coefficient of the nonlinear damper. T To test the axial tensile force of the object, xa This indicates the installation location of the damper.

2. The parameter design method according to claim 1, characterized in that, In step S1, the damping coefficient of the nonlinear damper is obtained using the following formula. c : in, n For the front n First mode, L The effective length of the test object, m To test the mass per unit length of the object, T To test the axial tensile force of the object, xa This indicates the installation location of the damper.

3. The parameter design method according to claim 1, characterized in that, Before step S1, the theoretical modal damping ratio of the nonlinear viscous inertial mass damper is obtained. If the low-order modal damping in the theoretical modal damping ratio does not meet the preset design requirements, then step S1 is executed.

4. The parameter design method according to claim 3, characterized in that, The theoretical modal damping ratio is calculated using the following formula. : in, Where is the vibration frequency, and c is the damping coefficient of the nonlinear damper. , n For the front n First mode, L The effective length of the test object, m To test the mass per unit length of the object, xa This refers to the installation location of the damper. T To test the axial tensile force of the object, , .

5. A parameter design system for a nonlinear viscous inertial mass damper, characterized in that, The nonlinear viscous inertial mass damper includes a nonlinear damper and an inertial mass unit, wherein the nonlinear damper and the inertial mass unit are connected in parallel, and the parameter design system includes: Adjustment module: Used to continuously adjust the velocity index in the nonlinear damping force formula. The formula for nonlinear damping force for; Where c is the damping coefficient of the nonlinear damper. The velocity at the damper endpoint; Calculation module: Used to calculate the adjustment velocity index using the free vibration decay method. The lower-order modal damping ratio is then used to obtain the velocity index that meets the preset design requirements. The pre-selected range; Acquisition module: used to acquire different speed indices within the preselected range. The corresponding reduction rate of higher-order modal damping ratio To obtain the reduction rate of the higher-order modal damping ratio Set, reduction rate of higher-order modal damping ratio The speed index corresponding to the minimum reduction rate that centrally meets the preset requirements This is the target speed index; Obtain different speed indices in the acquisition module. The corresponding reduction rate of higher-order modal damping ratio The reduction rate of the higher-order modal damping ratio is obtained using the following formula. : in, , For gamma function, Let n be the nth natural frequency of the cable when no damper is installed. The vibration amplitude at the damper installation location. for , c The damping coefficient of the nonlinear damper. T To test the axial tensile force of the object, xa This indicates the installation location of the damper.

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