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
- internal resonances
- nonlinear normal modes
Date of Defense 1997-02-27 Availability unrestricted AbstractThere is a need for reliable methods to determine
approximate solutions of nonlinear continuous
systems. Recently, it has been proved that
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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