应用于干摩擦振动系统中的Galerkin法
Galerkin Method Applied to the Vibration System with Dry Friction

DOI: 10.12677/OJAV.2019.74017, PP. 155-160

Keywords: 干摩擦，Fourier级数，Galerkin法，Broyden法
Dry Friction, Fourier Series, Galerkin Method, Broyden Method

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Abstract:

本文主要研究一个受干摩擦作用的振动系统的周期解的近似求解。此系统的周期解近似地表示Fourier级数，并通过Galerkin法把微分方程转换成非线性代数方程组，利用Broyden法来对此非线性代数方程组求解。最后数值积分的结果用来验证该方法的有效性。
In this paper, the approximate periodic solution of a vibration system subjected to dry friction is studied. The periodic solution of this system approximately represents the Fourier series, the dif-ferential equation is transformed into nonlinear algebraic equations by Galerkin method, and the nonlinear algebraic equations are solved by Broyden method. Finally, numerical integration results are used to verify the effectiveness of the method.

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