Mode Localization in a System of Coupled Flexible Beams with Geometric Nonlinearities

The localized free oscillations of two linearly coupled, flexible beams are studied. Geometric nonlinearities arising due to nonlinear relation between curvature and transverse displacement and longitudinal inertia are considered, the nonlinear partial differential equations of motion are discretized using the flexural modes of the linearized system, and an analysis is performed using the method of multiple‐scales. When the beams oscillate in their first primary modes, localized solutions are found which bifurcate from an antisymmetric mode. When the second and third flexural modes are taken into account, a low‐order internal resonance greatly affects the localization phenomenon, and stable branches of localized solutions are detected which bifurcate from a symmetric mode. As the position of the coupling stiffness approaches the node of the second linearized mode, a complicated series of bifurcation phenomena unfolds, including a degenerate, destabilizing „Hamiltonian Hopf bifurcation”.