基于谐波平衡法的微振动被动控制动力学研究

为了探究航天器被动隔振系统参数对隔振效果的影响，用变形的三次多项式函数描述粘弹性隔振器的非线性刚度，用分数导数阶算子表征隔振器的阻尼特性，建立了微重力状态下被动隔振系统非线性动力学模型，用谐波平衡法对动力学微分方程进行求解，计算隔振系统的振动传递率，然后探讨了隔振器以及隔振对象的刚度、阻尼、质量对隔振效果的影响。研究结果表明，隔振器非线性阻尼项对系统隔振效果影响很大，被隔振对象的质量对隔振系统共振峰值的影响与非线性阻尼系数的大小密切相关。

Research on Passive Control Dynamics of Micro-vibration Based on Harmonic Balance Method

For investigating the effects of passive vibration isolator parameters on the vibration transmissibility, nonlinear stiffness characteristics of the vibration isolating material was described by the cubic polynomial function of its deformation, and the nonlinear damping was characterized by viscoelastic fractional derivative operator. The nonlinear dynamic model in microgravity environment of passive vibration isolator system was developed．The dynamic response characteristics were analyzed by the harmonic balance method, and the vibration transmissibility was obtained. Then the influence of stiffness, damping and mass of the isolator and isolated body on vibration isolation effect were analyzed．The results provide theoretic reference for design of spacecraft isolators．The results show that the effects of vibration isolator nonlinear damping coefficient on vibration transmissibility were obvious and the effects of vibration isolation object mass on resonance vibration peak value have a great deal to do with the vibration isolator nonlinear damping coefficient.