Nonlinear Vibration of Buckled Beams

Abstract

The steady state response and stability of free and forced vibration of simply supported, axially restrained, buckled beams is investigated. The equations of motion dealing with the buckled state include the effect of an initial displacement either by initial load or by initial temperature. By an assumed mode solution, the response and stability of two types of vibration are determined—snap-through (symmetrical) and one-sided (unsymmetric) vibration. The theoretical results of the response and stability are verified by analog computer simulation. It is concluded that the stability of the unsymmetric vibration is not a problem and that the different orders of parametric response of the rest modes (the modes originally not excited) in symmetric vibration correspond to the instability regions determined for the approximate single mode response.