基于微分求积有限元法的双层微板系统振动特性研究

Application of differential quadrature finite element method to the free vibration analysis of double-layered microplate system

基于修正的偶应力理论和两变量精化的剪切变形理论,建立了由Winkler-Pasternak连续弹性夹层连接的双层微板系统的自由振动模型,着重推导了系统异步振动的运动微分方程和势能泛函。融合Gauss-Lobatto求积准则和微分求积准则构造了具有C~1连续性的微分求积有限元。通过与已有文献进行对比,验证了数值方法的有效性。详细讨论了各种因素对系统同步和异步振动特性的影响。结果表明,系统的自由振动特性对材料尺度参数、长宽比、长厚比以及边界条件呈现出依赖性;弹性夹层刚度仅对系统异步振动产生作用;随着模态阶次的增大,材料尺度参数和弹性夹层刚度对异步振动频率和模态的影响变得显著。

This paper developed the free vibration model of a double-layered microplate system connected by Winkler-Pasternak continuous elastic interlayer within the combined framework of the modified couple stress theory and a two-variable refined shear deformation theory.The derivation of differential equations of motion and potential energy for the asynchronous vibration of the system was emphasized.To solve the resulting boundary value problem,the differential quadrature finite element with C 1 -continuity was constructed by combining differential quadrature and Gauss-Lobatto quadrature rules.The efficacy of our solution method was demonstrated by comparing its predictions with the available ones.The effects of various factors on the system’s synchronous and asynchronous vibration characteristics were discussed in detail.It is revealed that:(1) the double-layered microplate system’s vibration characteristics depend on the material length scale parameter,length-to-width ratio,length-to-thickness ratio and boundary conditions;(2) the elastic interlayer stiffness only affects the asynchronous vibration characteristics of the system;(3) size effects on the vibration frequencies and mode shapes become noticeable as the material length scale parameter or the elastic interlayer stiffness increases.