Pre-buckling Transverse Free Vibration of an Asymmetrically Supported Euler Beam Subjected to Distributed Follower Forces

摘要

Based on the accurate geometrical theory for the extensible elastic beams, an exact mathematical model of post-buckling transverse free vibration of Euler beams subjected to a distributed tangential follower force along the central axis are established. By using shooting method, pre-buckling free vibrations of both simply supported and fixed Euler beam are solved and the responses of small amplitude vibration are obtained. The numerical results show that all the frequencies of unbuckled beams decrease continuously with the increment of the load parameters.