Nonlinear Vibrations of a Beam With Pinned Ends

Abstract

This paper describes theoretical and experimental investigations of the large-amplitude vibrations of a flexible beam simply supported on a nearly rigid base. The beam is designed to minimize most secondary effects, such as transverse shear flexibility, rotatory inertia, and nonlinearities in curvature and in the stress-strain curve. Detailed attention is given to quantitative verification of the assumptions made in deriving the equation of motion. Three different approaches are used to solve the equation: assumed-space mode, assumed-time mode, and Ritz-Galerkin solutions. In the experiments, the beam was base excited. The resonant frequencies and associated strain distributions, modal shapes, and waveforms were measured for various values of initial tension and amplitude ratios (ratio of maximum amplitude to beam thickness) up to 16. Within experimental accuracy, the experimental results verified all of the assumptions made in the analyses. However, no one method of solution resulted in the best predictions of all of the experimentally observed phenomena.