A Theoretical and Experimental investigation of Nonlinear Vibrations of Buckled Beams

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Engineering Science and Mechanics

Department dc:contributor.department

Engineering Science and Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1997

Author dc:creator

• Lacarbonara, Walter

Chair dc:contributor.committeechair

• Nayfeh, Ali H.

Committee members dc:contributor.committeemember

• Ragab, Saad A.
• Batra, Romesh C.

• direct approach
• galerkin discretization
• post-buckling
• internal resonances
• nonlinear normal modes

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-441520272974850

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/36721