Dynamics of three-degree-of-freedom systems with quadratic nonlinearities

The dynamics of two three-degree-of-freedom systems with quadratic nonlinearities are studied. The first system has two simultaneous two-to-one internal resonances. The second has a combination internal resonance. In both cases the response to a primary resonant excitation of the third mode is studied. The method of multiple time scales is used to obtain the equations that govern the amplitudes and phases of the first system. Then the fixed points of these equations are obtained and their stability is determined. The fixed points undergo Hopf bifurcations, and the overall system response can be periodic or periodically, quasiperiodically, or chaotically modulated. The method of the time-averaged Lagrangian is used to obtain the equations that govern the amplitudes and phases of the second system. The fixed points of these equations are obtained and their stability is determined. These fixed points undergo Hopf bifurcations, and the overall system response can be periodic or a two- or three-torus.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1991

Author dc:creator

• Nayfeh, Tariq Ali

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Language dc:language.iso

en

Dc Identifier Other

etd-10222009-125017

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/45246