计及表面残余应力的旋转凸凹型纳米圆板失稳分析  

Instability Analysis of Rotating Convex and Concave Circular Nanoplate by Considering Surface Residual Stress

作　　者：杨勇强[1] 杨萍[2] 张旭乐 YANG Yongqiang;YANG Ping;ZHANG Xule(College of Mechanical&Electrical Engineering,Shaanxi University of Science&Technology,Xi′an 710021,China;School of Electronic Information and Artificial Intelligence,Shaanxi University of Science&Technology,Xi′an 710021,China)

机构地区：[1]陕西科技大学机电工程学院,西安710021 [2]陕西科技大学电子信息与人工智能学院,西安710021

出　　处：《机械科学与技术》2024年第3期409-415,共7页Mechanical Science and Technology for Aerospace Engineering

基　　金：陕西科技大学博士基金项目(2020BJ-02);陕西省教育厅服务地方专项(21JC004)。

摘　　要：根据纳米材料表面残余应力和弹性板小挠度理论,建立旋转凸凹型纳米圆板横向振动微分方程,采用微分求积法得到不同条件下凸凹型纳米圆板的无量纲复频率随无量纲角速度和无量纲表面残余应力参数变化情况。研究结果显示:在周边固支和简支条件下,旋转凸凹型纳米圆板均发生第1阶发散失稳现象。在其他条件一定的情况下,周边固支凹型纳米圆板的临界失稳角速度小于凸型纳米圆板,周边简支凹型纳米圆板的临界失稳角速度大于凸型纳米圆板。临界失稳角速度随着表面残余应力的增加而增大,临界表面残余应力随着无量纲角速度的增加而增大。Based on the theory of the surface residual stress of nanomaterials and small deflection of elastic plate,the transverse vibration differential equation of rotating convex-concave circular nanoplate was established.The variation of dimensionless complex frequency of convex-concave circular nanoplate with dimensionless angular speed and surface residual stress under different conditions was obtained by using the differential quadrature method.The results show that the first-order divergence instability of rotating convex-concave circular nanoplate was observed in both clamped and simply supported conditions.When other parameters are constant,the critical instability angular speed of the clamped concave circular nanoplate is smaller than that of the convex circular nanoplate,and the critical instability angular speed of the simply supported concave circular nanoplate is greater than that of the convex circular nanoplate.The critical instability angular speed increases with the increasing of surface residual stress,and the critical surface residual stress increases with the increasing of dimensionless angular speed.

关 键 词：纳米圆板 横向振动 表面残余应力 发散失稳 

分 类 号：O327[理学—一般力学与力学基础]