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 Nano-plate by Considering Surface Residual Stress
杨勇强 1杨萍 2张旭乐1
作者信息
- 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
- 折叠
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.
Abstract
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Key words
circular nanoplate/transverse vibration/surface residual stress/divergence instability引用本文复制引用
基金项目
陕西科技大学博士基金(2020BJ-02)
陕西省教育厅服务地方专项(21JC004)
出版年
2024
国家科技期刊平台
NSTL
万方数据