连结子结构在非线性动力学分析中的应用

APPLICATION OF LINK SUBSTRUCTURE TO NONLINEAR DYNAMIC SYSTEM ANALYSIS

提出一种由线性连接元和非线性连接元组成的连接子结构 ,并将这种连接子结构用于自由界面的模态综合技术 .利用非线性振动理论的平均方法 ,求得经模态综合法降维后系统方程的近似解析解 .从而将具有连接子结构的自由界面的模态综合技术推广应用到具有局部非线性的复杂结构系统的动力分析 ,为利用非线性振动理论的平均方法及动力系统理论进一步研究高维非线性动力学系统的振动特性、分岔及混沌行为建立了新的途径 .算例表明 ,该方法具有足够的精度 .

A link substructure composed of a group of linear and nonlinear link units,can be used in the free interface modal synthesis technique to set up nonlinear vibration equations.Then the problem is reduced to less degrees of freedom to solve nonlinear equations by the modal synthesis method.To verify the successfulness of this method,an example is given.The approximate analytic solution of the low dimensional system has been obtained by KMB averaging method.Hence the free interface modal synthesis technique using link substructures is extended to the dynamic analysis of the structures with local non linearity.This approximate method can also be used to study the bifurcation and chaos behavior of high dimensional systems with local nonlinear properties.The calculating example indicates that this method has enough precision.