一种质点和刚体组合的非线性振动分析

Analysis of vibrational characteristics for an equipment composed of a mass point and a rigid body

对于力学中的非线性振动问题,一般教材上都是用一微分方程来表示其运动规律,而没有进行求解.为解决这一类型问题,本文将通过一实例分析给出一种解决方案.首先给出了一种质点和刚体组合的振动装置,然后运用牛顿力学规律求出其运动微分方程,并采用迭代的方法利用数学工具MATLAB进行了编程计算,得到了系统运动在无阻尼和有阻尼两种情况下的的相图和振动曲线,最后对结果进行了比较和讨论.

For the mechanical problems of nonlinear vibration, the kinematic laws are usually expressed as a differential equation without result in teaching materials. In order to solve this type of problems, we give a Solution through the analysis of an example in the paper. First we present a vibrational equipment composed of a mass point and a rigid body, then we establish a differential equation based on the fundamentals of Newtonian mechanics. By using iterative method and using MATLAB we perform the calculation, we give the phase diagram and oscillating characteristic of the system under two conditions that there is no damping and thereis damping. In the end we compare and discuss the results.