含负刚度器件的Maxwell模型动力吸振器的参数优化

将黏弹性材料模型中的Maxwell模型引入到吸振系统中，形成一种含负刚度器件的Maxwell模型动力吸振器，并对该模型的参数进行优化。首先，建立系统的运动微分方程，得到系统的解析解。然后，利用固定点理论将系统的三个固定点调整到同一高度，求出系统的最优频率比和最优负刚度比，并根据H∞优化准则得到系统的最优阻尼比。最后，分别在简谐激励和随机激励条件下，与几种经典动力吸振器模型对比证明了含负刚度的Maxwell模型动力吸振器有较好的吸振效果。
Abstract：The maxwell model of the viscoelastic material was applied to a dynamic vibration absorber (DVA) system to form a Maxwell model dynamic vibration absorber with negative stiffness spring,and the parameters of the model were optimized. At first,the analytical system solution was obtained based on the established motion differential equation. Then,three fixed points were found in the amplitude-frequency curves of the primary system. The design formulae for the optimal tuning ratio of the DVA were obtained by adjusting the three fixed points to the same height according to the fixed-point theory. According to the characteristics of negative stiffness elements,the optimal negative stiffness ratio was obtained and it could keep the system stable. The optimal damping ratio was obtained by minimizing the maximum value of the amplitude frequency curves. At last,the comparisons of the presented DVA with three other traditional DVAs under the harmonic and random excitations show that the presented DVA in this paper performs better in vibration absorption.