受集中力质量在受分布力弦上移动时的振动响应分析

摘要

A semi-analytical method was developed for solving vibration responses of a mass subjected to a concentrated force movingon a string with distributed load.Firstly,the differential vibration equation was built according to their mechanical model.Then the matrix differential equation was derived by using Fourier transformation,and it was numerically solved with Newmark method.To validate the semi-analytical method and its results,the vibration equation's analytical solution was deduced under some particular conditions.The results with the semi-analytical method were compared with those using the analytical solution and those in literatures,the correctness of the semi-analytical method was verified.%针对受集中力质量在受分布力弦上移动时的振动响应问题，发展了一种半解析求解方法。首先根据力学模型建立了振动方程，然后利用傅里叶变换得到了方程的矩阵形式，并采用 Newmark 方法编程进行了数值求解。同时为验证方法的正确性，针对特定条件下的振动方程推导了解析解。最后通过半解析求解结果与解析解和文献的对比分析，验证了该方法的正确性。