Type of Document	Master's Thesis
Author	Lacarbonara, Walter
URN	etd-441520272974850
Title	A Theoretical and Experimental investigation of Nonlinear Vibrations of Buckled Beams
Degree	Master of Science
Department	Engineering Science and Mechanics
Advisory Committee	Advisor Name Title Batra, Romesh C. Ragab, Saad A. Nayfeh, Ali H. Committee Chair
Keywords	direct approach galerkin discretization post-buckling internal resonances nonlinear normal modes
Date of Defense	1997-02-27
Availability	unrestricted
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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