Natural Frequencies Analysis for a Beam Subjected to Moving Distributed Mass with Time-dependent Velocity

摘要

In this paper, the natural frequencies analysis is conducted by applying the dynamic stiffness method and Wittrick-Williams algorithm for a beam subjected to moving distributed mass, which arises for extensive engineering problems such as train-bridge system, pipeline transporting oil, and so on. The time domain partial differential equation was firstly transferred to frequency domain ordinary differential equation based on the method of variables separation. In order to make the key factors of the system clearer, normalization procedure was carried to the frequency domain equations. The dynamic stiffness matrix was then deducted after introducing the displacement and force boundary condition, and the natural frequencies of the system was calculated using Wittrick-Williams algorithm. The comparison with the FEM results validated the presented method, and proved it with higher precision. In addition, the rules of natural frequencies varying with velocity, acceleration, destiny of moving distributed mass were brought forth according to this method.