Research On Vibration Control And Dynamics Of Viscoelastic System

Viscoelastic materials play a key role in improving the vibration control effect of mechanical structural system due to their good vibration damping performance.In order to improve the vibration damping performance of the system,the viscoelastic Maxwell element is first applied to the linear dynamic vibration absorber to research its vibration damping performance,and then the viscoelastic Maxwell element is introduced into the nonlinear system for approximate solution and analysis of its nonlinear dynamic behavior.Finally,the viscoelastic Maxwell element is introduced into nonlinear energy sink for vibration damping analysis.The main research contents of this thesis are as follows.(1)A new dynamic vibration absorber with viscoelastic Maxwell element is researched.The optimal frequency ratio,optimal stiffness ratio and optimal damping ratio of the system are obtained by using fixed-point theory and H_∞optimization criterion,and the system response changes under different optimal solutions are considered.In the process of optimization,the optimal working range of the inerter ratio is determined based on the conventional parameters.This thesis discusses the value of the inerter ratio within and outside the optimal working range,and analyzes the influence of the inerter ratio on the vibration reduction effect of the system.Finally,the damping performance of the model and the traditional dynamic vibration absorbers under harmonic excitation and random excitation is analyzed and compared.(2)The main resonance and stability of nonlinear viscoelastic Zener model are investigated.Based on the traditional multi-scale method,the multi-scale method is extended and used to study the nonlinear odd-order differential equation and the dynamic problems of the nonlinear odd-order system are solved.Taking the nonlinear viscoelastic Zener model as an example,the correctness of the analytical process of the extended method is verified and the stability of the steady-state periodic solution is analyzed based on the Lyapunov first method.Finally,the effects of nonlinear term,external excitation,the stiffness and damping coefficients of Maxwell element on the dynamic behavior and stability of the system are analyzed by simulation.(3)The dynamic behavior of homoclinic bifurcation and chaos in nonlinear Zener model under harmonic excitation is considered.The analytically necessary condition for chaos in the sense of Smale horseshoe is derived based on Melnikov method,and the parameters are selected for numerical simulation according to the conditions and the main resonance conditions.From the bifurcation diagram and the maximum Lyapunov exponent spectrum,the path of the system to chaos is deeply discussed.Finally,the effects of nonlinear term,stiffness coefficient and damping coefficient of Maxwell element on the necessary conditions for chaos are analyzed respectively.(4)The damping performance of nonlinear energy sink with viscoelastic Maxwell element is studied.The amplitude frequency response curve of the system is obtained by harmonic balance method and the correctness of the analytical solution is verified by the numerical method.Compared with the traditional nonlinear energy sink,the damping performance of viscoelastic nonlinear energy sink and the change of system response under different parameters are analyzed.Finally,the variation trend of vibration reduction effect when the nonlinear stiffness ratio and damping ratio change at the same time under different mass ratios is analyzed,and the optimal value range of viscoelastic nonlinear energy sink is discussed.Finally,the advantages of viscoelastic Maxwell element in vibration reduction are summarized in detail,and the performance of viscoelastic materials in linear and nonlinear systems and their broad application prospects are explained.And the problems of viscoelastic materials in solving parametric vibration in the field of vibration control are prospected.