Nonlinear Vibrations of a Beam Under Harmonic Excitation

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.