考虑表面效应的纳米圆形薄板振动

基于Gurtin的表面弹性理论考虑表面弹性和残余表面应力,建立周边固支的轴对称纳米圆板的振动微分方程。研究残余表面应力对纳米板振动频率和主振型的影响。结果表明:前四阶固有频率分别随着残余表面应力参数的增大而减小;但残余表面应力对一阶固有频率和主振型影响最大,随着振动阶数的增大,残余表面应力对固有频率和主振型的影响逐渐减小;同时对于一阶固有频率,板的厚度越薄或者板的半径越大,受残余表面应力的影响越大。
Based upon Gurtin 's theory of surface elasticity, the surface elasticity and residual surface stress are both considered, and the vibration model of a thin axi-symmetric plate at nano-scale with clamped boundary condition is developed. The influences of the residual surface stress effect on the first four order natural frequencies and vibration modes were presented. The results reveal that the first order natural frequency decreases with the increase of the residual surface stress parameter. Moreover, the residual surface stress effect exerts more important effect on the first natural frequency than others, and with the vibration order increases, the effect becomes weaker. The first four order vibration modes for various surface effect parameters are also given in the paper, and the impact on the vibration mode is similar to that on the natural frequencies. The influence of the residual surface stress is greater on the first main mode than other modes