Scholarly Communications Project


A Theoretical and Experimental Investigation of Nonlinear Vibrations of Buckled Beams

by

Walter Lacarbonara

Master's Thesis submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of

Master of Science

in

Engineering Science and Mechanics

Approved

Ali H. Nayfeh, Chair
Romesh C. Batra
Saad A. Ragab

February 27, 1997
Blacksburg, Virginia


Abstract

There is a need for reliable methods to determine approximate solutions of nonlinear continuous systems. Recently, it has been proved that finite-degree-of-freedom Galerkin-type discretization procedures applied to some distributed-parameter systems may fail to predict the correct dynamics. By contrast, direct procedures yield reliable approximate solutions. Starting from these results and extending some of these concepts and procedures, we compare the outcomes of these two approaches (the Galerkin discretization and the direct application of a reduction method to the original governing equations) with experimental results. The nonlinear planar vibrations of a buckled beam around its first buckling mode shape are investigated. Frequency-response curves characterizing single-mode responses of the beam under a primary resonance are generated using both approaches and contrasted with experimentally obtained frequency-response curves. It is shown that discretization leads to erroneous quantitative as well as qualitative results in certain ranges of the buckling level, whereas the direct approach predicts the correct dynamics of the system.

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