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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。
Nonlinear vibration of beam with longitudinal dry friction boundary conditions is studied. The constitutive relations of dry friction are respectively described as sticking-sliding state, transient sliding state and sticking state. Firstly, the dynamic equations of the beam and the boundary conditions of the dry friction force are established by the Hamilton principle, and then the nonlinear ordinary differential equations are obtained by means of the Galerkin method. The fundamental steady wave response of the system is solved by harmonic balance principle, and the stability conditions of the solution are discussed. Numerical calculation using turbo-C language on the computer to complete, which obtained when the friction parameters change several typical frequency response curve.