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

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''.