Background As a random search algorithm based on natural phenomena and biological intelligence, swarm intelligence optimization algorithm could provide a new solution for combinatorial optimization problems on the basis of traditional techniques. The particle swarm algorithm which simulates the foraging behavior of birds has achieved good results in finding the global optimal solution. Purpose In this paper, a kind of viscoelastic Maxwell type dynamic vibration absorber model with inerter is investigated under the combination of traditional theory and intelligence algorithm. Methods The optimization design of DVA considers the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1869_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">$\varvec{H_{\infty }}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold-italic">H</mi> <mi mathvariant="bold-italic">∞</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> optimization criterion. Based on the basic optimal expressions of the system parameters obtained by the fixed point theory, we innovatively introduce the particle swarm intelligence algorithm, and comprehensively analyze all the optimization situations of single variables and combined variables. It is proved that the algorithm can actively adjust the parameter values to minimize the maximum amplitude. Furthermore, the fourth order Runge-Kutta method is used to simulate the numerical solution and the analytical solution to verify the parameter values. Results The numerical results present the consistency and effectiveness of the analytical solution and the numerical solution. Compared with other classical models, the amplitude frequency responses, time histories and vibration reduction effect of the primary system of different models under harmonic excitation and random excitation are studied. Conclusions Numerical simulations of the displacement variance and attenuation ratio of the primary system during dynamic time comparisons with different DVAs indicate that the DVA presented in this paper has more satisfactory control performance. The inerter element can indeed provide a favorable effect for the vibration reduction of absorber. The combination of basic theory and intelligent algorithm of active regulation to solve the vibration control in engineering application field is the biggest innovation. The research results could provide theoretical and calculation basis for the optimal design of vibration absorber.

Optimization and Application of Particle Swarm Intelligence Algorithm in Maxwell Type Dynamic Vibration Absorber with Inerter Element

期刊论文
发表日期：

2025年5月9日

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Yuying Chen,
Hongzhen Zhao,
Jianjun Zhang,
Huimin Zhou,
Han Sun

摘要

Background

As a random search algorithm based on natural phenomena and biological intelligence, swarm intelligence optimization algorithm could provide a new solution for combinatorial optimization problems on the basis of traditional techniques. The particle swarm algorithm which simulates the foraging behavior of birds has achieved good results in finding the global optimal solution.

Purpose

In this paper, a kind of viscoelastic Maxwell type dynamic vibration absorber model with inerter is investigated under the combination of traditional theory and intelligence algorithm.

Methods

The optimization design of DVA considers the $\varvec{H_{\infty }}$ $H_{\infty}$ optimization criterion. Based on the basic optimal expressions of the system parameters obtained by the fixed point theory, we innovatively introduce the particle swarm intelligence algorithm, and comprehensively analyze all the optimization situations of single variables and combined variables. It is proved that the algorithm can actively adjust the parameter values to minimize the maximum amplitude. Furthermore, the fourth order Runge-Kutta method is used to simulate the numerical solution and the analytical solution to verify the parameter values.

Results

The numerical results present the consistency and effectiveness of the analytical solution and the numerical solution. Compared with other classical models, the amplitude frequency responses, time histories and vibration reduction effect of the primary system of different models under harmonic excitation and random excitation are studied.

Conclusions

Numerical simulations of the displacement variance and attenuation ratio of the primary system during dynamic time comparisons with different DVAs indicate that the DVA presented in this paper has more satisfactory control performance. The inerter element can indeed provide a favorable effect for the vibration reduction of absorber. The combination of basic theory and intelligent algorithm of active regulation to solve the vibration control in engineering application field is the biggest innovation. The research results could provide theoretical and calculation basis for the optimal design of vibration absorber.