Investigations of natural frequencies and vibration mode shapes for a post-buckled beam with different attached masses
This paper considers the theoretical response of a baseexcited post-buckled beam. A mass that can be varied was attached to the midspan of the clamped-clamped beam. The theoretical model for the post-buckled beam was first investigated by applying the extended Hamilton principle to obtain a partial differential equation for beam motion carrying a central mass. This equation was used to analyze the behavior of the pre- and post-buckled natural frequencies in terms of the axial load. The first three buckled configurations were then examined, and plots showing the pre- and post-buckled modal frequencies were constructed. It was found that the addition of a central mass to the beam significantly lowered its first natural frequency, while the second frequency was relatively unaffected. A set of experiments were performed and it was shown that adding a mass on the beam increased the occurrence of snap through behavior. This nonlinear behavior produced large displacements and chaotic behavior. Copyright © 2010 by ASME.
