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.

A straight beam with fixed ends, excited by the periodic motion of its supporting base in a direction normal to the beam span, was investigated analytically and experimentally. By using Galerkin’s method (one mode approximation) the governing partial differential equation reduces to the well-known Duffing equation. The harmonic balance method is applied to solve the Duffing equation. Besides the solution of simple harmonic motion (SHM), many other branch solutions, involving superharmonic motion (SPHM) and subharmonic motion (SBHM), are found experimentally and analytically. The stability problem is analyzed by solving a corresponding variational Hill-type equation. The results of the present analysis agree well with the experiments.