面内平动黏弹性板非线性振动的内-外联合共振

研究了同时存在受迫共振和1∶3内共振时的面内平动黏弹性板的横向非线性振动问题．板的黏弹性材料用Kelvin本构关系描述．基于系统的运动方程和四边简支的边界条件，对偏微分方程应用直接多尺度法建立了联合共振时的可解性条件．应用Routh-Hurvitz判据对系统幅频响应的稳定性进行了判别．给出了黏弹性系数、面内平动速度和激励幅值3个参数对幅频响应的影响．最后，应用微分求积数值方法验证了近似解析方法的结论.

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

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.