The nonlinear nonplanar oscillations of cantilever beams excited by a combination parametric resonance are investigated. The effect of geometric and inertia nonlinearities in the governing equations of motion and boundary conditions is considered. The method of multiple scales is directly applied to the partial-differential equations and boundary conditions to derive the equations governing the modulations of the amplitudes and phases of the interacting modes. Then, the influence of the forcing amplitude and frequency on the response is analyzed. The results show that, through this mechanism, a small-amplitude high-frequency excitation can produce a large-amplitude low-frequency response, which cannot be predicted by linear theory.
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