基于Shaw不变流形的双层金属橡胶隔振系统振动响应分析

RESEARCH OF TWO DOF METAL RUBBER VIBRATION ISOLATION SYSTEM BASED ON SHAW INVARIANT MANIFOLDS

多自由度非线性系统求解是困扰其推广使用的难题,为解决多自由度金属橡胶非线性隔振系统特性分析与响应计算问题,采用基于Shaw不变流行定义的非线性模态理论来求解双层金属橡胶隔振系统的振动响应。首先基于金属橡胶双折线本构关系模型建立了双层金属橡胶隔振系统的力学模型,并对金属橡胶迟滞环节进行了等效线性化,推导了隔振系统的运动微分方程;然后依据Shaw不变流行的定义,提出了能使非线性模态理论成立的基本假设,推导了该系统的非线性模态方程,并指出了用非线性模态叠加法求解的过程;最后分别用该方法与Runge-Kutta数值计算方法求解了算例,并将结果进行对比,说明了以非线性模态叠加法求解两自由度金属橡胶隔振系统响应的可行性,尽管该方法尚不能十分精确,但在多自由度非线性系统求解没有较好的办法的现状下,为解决多自由度金属橡胶振动系统响应计算问题打下了基础,该方法对多自由度非线性系统的求解具有重要的意义。

The characteristic analysis and response calculation of the multi-DOF nonlinear vibration isolation system was a difficult problem which blocks the popularization and application of the system, in order to solve the problem of multi-DOF metal rubber nonlinear vibration isolation system, the nonlinear modal theory based on Shaw invariant manifolds was used to solve the response of one double layer metal rubber vibration isolation system in this paper. Firstly, The mechanical model of the double layer metal rubber vibration isolation system was established, which based on the hysteresis link of the metal rubber, and the hysteresis link was equivalent linearization, then the simplified differential equation of the system was deduced. Secondly, the basic assumptions which could make nonlinear modal theory be right were put forward based on the definition of the invariant manifolds, then the nonlinear modal equation of the system was deduced and the process of solving response of the system using nonlinear modal superposition method was point out. Finally, the results of solving an example by using the method in this paper and the numerical calculation were compared, it showed that the nonlinear modal superposition method was useful to solve the response of the double layer metal rubber vibration isolation system. Although it was not completely accurate, it could also lay the foundation of solving the problem of multi-DOF nonlinear vibration isolation system, The method proposed in this paper has important signification to the solving of the characteristic analysis and response calculation problem of the multi-DOF nonlinear vibration isolation system in the existing conditions.