具有初挠度夹层圆板的亚谐波共振

Nonlinear Subharmonic Resonance of Circular Sandwich Plates with Initial Deflection

利用Galerkin法和L-P摄动法得出了具有初挠度夹层圆板的三阶亚谐解,用多尺度法讨论了解的稳定性。研究表明,大挠度软夹心夹层圆板会产生与材料非线性圆板类似的非线性亚谐振动现象,只有当激振力频率的1/3与圆板系统的固有频率之差即微小参量εδ增大到一定值时才会激发亚谐波共振,当夹层板系统的刚度减小,初挠度增大时,更容易激发其三阶亚谐波共振,出现多值与跳跃现象。稳定状态与初始条件和外激励有关。

Using Galerkin and the LP perturbation method,the periodical solutions which are nonlinear 1/3 subharmonic resonance for circular sandwich plate were obtained.The stability of the solutions was discussed with multi-scale method.The studies showed that large deflection of circular sandwich plate of soft sandwich was similar to circular plate with material nonlinearity for nonlinear sub-harmonic vibration,and only when the value of εδ increased to a certain sub-harmonic resonance could be spurred.When the stiffness of sandwich panel systems reduced,initial deflection increased,more prone to the third-order sub-harmonic resonance,there was more value with the jump phenomenon.Steady state was affected by the initial conditions and external excitation.