TANG You-qi, CHEN Li-qun. Internal-External Combination Resonance of Nonlinear Vibration of in-Plane Translating Viscoelastic Plates[J]. Applied Mathematics and Mechanics, 2013, 34(5): 480-487. doi: 10.3879/j.issn.1000-0887.2013.05.006
Citation: TANG You-qi, CHEN Li-qun. Internal-External Combination Resonance of Nonlinear Vibration of in-Plane Translating Viscoelastic Plates[J]. Applied Mathematics and Mechanics, 2013, 34(5): 480-487. doi: 10.3879/j.issn.1000-0887.2013.05.006

Internal-External Combination Resonance of Nonlinear Vibration of in-Plane Translating Viscoelastic Plates

doi: 10.3879/j.issn.1000-0887.2013.05.006
  • Received Date: 2013-04-02
  • Rev Recd Date: 2013-04-20
  • Publish Date: 2013-05-15
  • Nonlinear vibrations of inplane translating viscoelastic plates were investigated on the steady-state responses in external and internal resonances. The plate’s material obeys the Kelvin model in which the material time derivative was used. Based on the governing equation and boundary conditions for four edges simple supports, the method of multiple scales is applied to establish the solvability conditions in the primary resonance and the 3:1 internal resonance. The RouthHurvitz criterion is used to determine the stabilities of the steadystate responses. The effects of the viscosity coefficient, the in-plane translating speed, and the excitation amplitude on the steadystate responses are examined. The differential quadrature scheme is developed for the plate model to solve the nonlinear governing equations numerically. The numerical calculations confirm the approximate analytical results regarding the solutions of the steady- responses.
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