Nonlinear Vibrations of a Buckled Beam Under Harmonic Excitation

Abstract

A buckled beam with fixed ends, excited by the harmonic motion of its supporting base, was investigated analytically and experimentally. Using Galerkin’s method the governing partial differential equation reduced to a modified Duffing equation, which was solved by the harmonic balance method. Besides the solution of simple harmonic motion (SHM), other branch solutions involving superharmonic motion (SPHM) were found experimentally and analytically. The stability of the steady-state SHM and SPHM solutions were analyzed by solving a variational Hill-type equation. The importance of the second mode on these results was examined by a similar stability analysis. The Runge-Kutta numerical integration method was used to investigate the snap-through problem. Intermittent, as well as continuous, snap-through behavior was obtained. The theoretical results agreed well with the experiments.