具有复杂边界条件的杆的振动分析

本文研究一端带有集中质量并支以弹簧另一端作支承运动的杆的纵向振动.由于这个问题的边界条件比较复杂,且要考虑阻尼,因此本文只求稳态周期解.首先分析线性系统;然后考虑材料非线性,用摄动法求具有非线性边界条件的非线性方程的近似解析解.

Vibration Analysis of a Rod with Complex Boundary Conditions

This paper deals with the forced longitudinal vibration of a rod carrying a concentrated mass and supported by a spring at one end. The vibration of the rodis excited by the motion of the support point at the other end Since the boundary conditions of the problem are complex and it is necessary to consider the damping, we determine only the steady state periodic solution. First the linear system is analysed; then the material nonlinearity is considered and the approximate analytic solution of nonlinear partial differential equation with nonlinear boundary conditions is obtained by the perturbation method.