Title page for ETD etd-441520272974850

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
  • direct approach
  • galerkin discretization
  • post-buckling
  • internal resonances
  • nonlinear normal modes
Date of Defense 1997-02-27
Availability unrestricted
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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