摘要
本文导出了一种适用于具有分块线性的复杂结构的非线性振动问题的非线性模态综合法。该法以连接各块的非线性元件的变形量为广义坐标,应用各分块构成的线性子系统的模态特性和非线性连接元件的本构关系建立了积分型的综合方程组。为了提高综合精度,方程组中考虑了各子系统的由高阶模态影响所形成的剩余柔度矩阵。由于以连接元件的变形量为广义坐标,使方程的数目与元件数目相同,从而缩小了解题的规模,提高了效率。文中给出了几个典型的应用算例,证明了本文理论的正确性。
In this paper,a new method of nonlinear modal synthesis for nonlinear systems of piece-by-piece linearity is derived,which takes the deformations of the nonlinear links as the generalized coordinates,i.e.,the number of equations is just the number of links connecting pieces,which makes the method more efficient for large and complex structures.The synthesis equation set in integration expression is based on the modal characters of the pieces and the inherent relations of the links.In order to improve the accuracy,the residual mobility by high-order modes is considered.The theory in this paper can be used to solve such problems as nonlinear coupling of linear systems,gapes, friction,and collisions.A powerful program based on the theory has been built up on IBM PC computers and checked by Van Der Pol's Oscillator and a multi-degree system of nonlinearity.
出处
《振动与冲击》
EI
CSCD
北大核心
1991年第4期22-30,共9页
Journal of Vibration and Shock
