MODE LOCALIZATION IN A SYSTEM OF COUPLED FLEXIBLE BEAMS WITH GEOMETRIC NONLINEARITIES

Authors
Citation
M. King et A. Vakakis, MODE LOCALIZATION IN A SYSTEM OF COUPLED FLEXIBLE BEAMS WITH GEOMETRIC NONLINEARITIES, Zeitschrift fur angewandte Mathematik und Mechanik, 75(2), 1995, pp. 127-139
Citations number
18
Categorie Soggetti
Mathematics,"Mathematical Method, Physical Science",Mechanics,Mathematics
ISSN journal
00442267
Volume
75
Issue
2
Year of publication
1995
Pages
127 - 139
Database
ISI
SICI code
0044-2267(1995)75:2<127:MLIASO>2.0.ZU;2-M
Abstract
The localized free oscillations of two linearly coupled, flexible beam s are studied. Geometric nonlinearities arising due to nonlinear relat ion between curvature and transverse displacement and logitudinal iner tia are considered, the nonlinear partial differential equations of mo tion are discretized using the flexural modes of the linearized system , and an analysis is performed using the method of multiple-scales. Wh en the beams oscillate in their first primary modes, localized solutio ns are found which bifurcate from an antisymmetric mode. When the seco nd and third flexural modes are taken into account, a low-order intern al resonance greatly affects the localization phenomenon, and stable b ranches of localized solutions are detected which bifurcate from a sym metric mode. As the position of the coupling stiffness approaches the node of the second linearized mode, a complicated series of bifurcatio n phenomena unfolds, including a degenerate, destabilizing ''Hamiltoni an Hopf bifurcation''.