基于修正偶应力和高阶剪切变形理论的变截面微梁的自由振动

基于修正偶应力和高阶剪切理论建立了仅含有一个尺度参数的Reddy变截面微梁的自由振动模型,研究了变截面微梁自由振动问题的尺度效应和横向剪切变形对自振频率计算的影响。基于哈密顿原理推导了动力学方程与边界条件,并采用微分求积法求解了各种边界条件下的自振频率。算例结果表明,基于偶应力理论预测的变截面微梁的自振频率均大于经典梁理论的预测结果,即捕捉到了尺度效应。另外,梁的几何尺寸与尺度参数越接近,尺度效应就越明显,而梁的长细比越小,横向剪切变形对自振频率的影响就越明显。

Free vibration analysis of non-uniform micro-beams based on modified couple stress theory and high order shear deformation theory

A free vibration model of micro non-uniform Reddy beam which contains only one internal material length scale parameter is developed based on the modified couple stress theory in conjunction with the high order shear deformation theory.The scale effects in the free vibration of non-uniform micro beams and the effect of transverse shear deformation on the natural frequencies are investigated.The Hamilton''s principle is employed to derive the equations and the boundary conditions.The differential quadrature method is employed to numerically solve the governing equations with different boundary conditions.Illustrative examples indicate that the natural frequencies predicted by the present model are always higher than that by classical theory,i.e.the scale effects are captured.Moreover,the closer the geometry size to the material scale length parameter,the more apparent the scale effects are,and the effects of transverse shear deformation are more apparent in smaller length-thickness ratios.