带集中质量共线杆系的动态响应分析

DYNAMIC RESPONSE ANALYSES OF COLLINEAR BARS WITH CONCENTRATED MASSES

带集中质量弹性杆的纵向振动在工程应用中是广泛存在而有待于深入研究的现象。考虑动力扰动是谐和的情况。首先写出问题的定解方程组,然后利用假设的带有未知系数的谐和解、问题的边界条件及集中质量处的动力学条件得到确定未知系数的线性代数方程组并求解,得到了问题的解析解。算例以三根杆、两个集中质量为例研究了杆件的振动位移幅度和动态应力幅度在不同频率扰动下沿杆轴方向的分布曲线,结论可为此类结构的动态强度校核和设计提供理论依据。

Longitudinal vibration of the elastic bars with concentrated masses widely exist in the engineering applications which needs to be studied deeply. In this paper,the harmonic dynamic disturbance was considered. At first,the equations to be determined were written out,the linear algebraic equations of the unknown coefficients were obtained utilizing the supposed harmonic solutions with unknown coefficients,boundary conditions of the problem and the dynamic conditions of the concentrated masses. The given example took three bars and two concentrated masses as the example,the vibration displacement amplitudes and the dynamic stress amplitudes of the bars along the axial direction with different disturbance frequencies were studied,The conclusions can provide the theoretical bases for the dynamic strength check and the strength design.