Non-linear interactions in asymmetric vibrations of a circular plate

摘要: Abstract In order to investigate the non-linear asymmetric vibrations of a clamped circular plate on an elastic foundation, primary resonances with internal resonance, in which natural frequencies two modes are commensurable considered. The response is expressed as expansion terms linear, free oscillation modes, and its amplitude considered be small but finite. method multiple scales used reduce governing equations system autonomous ordinary differential for phase variables. For numerical example case resonance (a relationship between frequencies), ω 32 ≈3 11 , where first subscript refers number nodal diameters second circles including boundary When frequency excitation near there exist at most five stable steady-state responses. Four them superpositions traveling wave components one superposition standing components. result shows interaction corresponding by showing non-vanishing amplitudes mode not directly excited. similarly shown exist. All responses excited indirectly, however, turn out unstable, peculiar phenomenon.