变截面二维功能梯度微梁的振动和屈曲特性北大核心CSCD

基于修正的偶应力理论和Timoshenko梁理论,应用变分原理建立了变截面二维功能梯度微梁的自由振动和屈曲力学模型.模型中包含金属组分和陶瓷组分的材料内禀特征尺度参数,可以预测微梁力学行为的尺度效应.采用Ritz法给出了任意边界条件下微梁振动频率和临界屈曲载荷的数值解.数值算例表明:微梁厚度减小时,无量纲一阶频率和无量纲临界屈曲载荷增大,尺度效应增强.锥度比对微梁一阶频率的影响与边界条件密切相关,同时,对应厚度和对应宽度锥度比的影响也有明显差异.变截面微尺度梁无量纲一阶频率随着陶瓷和金属的材料内禀特征尺度参数比的增加而增大,且不同边界条件时增大程度不同.厚度方向和轴向功能梯度指数对微梁的一阶频率和屈曲载荷也有显著的影响.

Vibration and Buckling Characteristics of 2D Functionally Graded Microbeams With Variable Cross Sections

Based on the modified couple stress theory and the Timoshenko beam theory, the free vibration and buckling mechanics model for 2D functionally graded microbeams with variable cross sections was established by means of the variational principle. The model contains the intrinsic material length scale parameters of the metal and ceramic components, which can predict the size effects of microbeams. The Ritz method was used to obtain the numerical solution of the vibration frequencies and critical buckling loads of the microbeams under arbitrary boundary conditions. Numerical examples reveal that, when the thickness of the microbeam decreases, the dimensionless 1st-order frequency and the dimensionless critical buckling load will increase, and the scale effect will grow larger. The effect of the taper ratio on the dimensionless 1st-order frequency of the microbeam is closely related to the boundary conditions. At the same time, the effects of the taper ratios of the thickness and the width are also significantly different. The dimensionless 1st-order frequencies of microbeams increase with the material length scale parameter ratios of ceramic and metal, and the degrees of increase are different under different boundary conditions. The thick-direction and axial material gradient indexes also have significant influences on the free vibration and buckling behavior of the microbeam.