干摩擦支承边界梁的非线性振动分析

Nonlinear Vibration Analysis of a Beam withSupporting of Dry Friction

研究梁具有纵向干摩擦边界条件时非线性振动。干摩擦力本构关系分别为粘住—滑动状态、瞬态滑动状态、粘住状态三种情形描述。首先由Ｈａｍｉｌｔｏｎ原理建立梁的动力学方程及其干摩擦力的边界条件，然后借助于Ｇａｌｅｒｋｉｎ法转化得到非线性常微分方程。采用谐波平衡原理进行系统的基波稳态响应求解，并讨论解的稳定性条件。数值计算利用ｔｕｒｂｏ－Ｃ语言在微机上完成，由此得到摩擦力参数改变时几种典型的频响特性曲线。

 study of nonlinear vibration of a beam with a boundary condition of axial dry friction is presented. The constitute relationships of dry friction are characterized by three possible states: stickslip state, transient slip state, and stick state. The governing equation for the beam is developed by Hamiltons principle, along with the boundary condition of dry friction force. The nonlinear ordinary differential equations then are derived by the Galerkin method. HBM is used to obtain the fundamental resonance response, and the stability conditions of the steady state solution are determined. Numerical simulations are conducted by TurboC program. Various of typical frequency response plots for different values of friction force parameters are given.