三层应变梯度微板系统的耦合振动特性

Coupled Vibration Characteristics of the Triple-Layered Strain Gradient Microplate System

基于修正的应变梯度理论和Kirchhoff-Love假设,建立了由Winkler-Pasternak弹性夹层连接的三层微板系统的耦合振动模型.结合Gauss-Lobatto求积准则和微分求积准则,构造了具有4节点108个自由度的C2连续性微分求积有限元,以求解微板系统的耦合振动边值问题.通过数值算例,验证了本文微分求积有限元法的有效性,讨论了各因素对微板系统振动频率及模态的影响.结果表明:微板系统发生完全同步振动时,弹性夹层不起作用;应变梯度效应或弹性夹层刚度不仅影响微板系统的各阶振动频率,而且会使系统产生模态跃迁现象;边界条件对微板系统振动频率计模态的影响显著.

Based on the modified strain gradient theory and the Kirchhoff-Love hypothesis,a coupled vibration model for a triple-layered microplate system connected by Winkler-Pasternak elastic interlayers is established.By combining the Gauss-Lobatto quadrature and the differential quadrature rules,a C 2 continuous differential quadrature finite element with 4 nodes and 108 degrees of freedom is constructed to solve the boundary value problem of the coupled vibration of the microplate system.Numerical examples validate the effectiveness of the differential quadrature finite element method proposed in this paper,and the influences of various factors on the vibration frequencies and modes of the microplate system are discussed.The results show that the elastic interlayers are ineffective during in-phase vibration of the microplate system.Both the strain gradient effect and the stiffness of the elastic interlayers affect not only the vibration frequencies of the microplate system at various orders but also induce mode jumping phenomena in the system.Boundary conditions significantly influence the vibration frequencies and modes of the microplate system.