变截面功能梯度Timoshenko梁的自由振动分析

基于梁物理中面的概念,使用哈密顿原理,推导得出轴向力作用下材料性质沿梁高变化的功能梯度材料(FGM)梁自由振动的控制微分方程组,然后求得该微分方程组的幂级数解.再基于弹性约束表示的一般边界条件得到频率方程.分析了长高比、梯度指数、轴向力以及截面变化系数等参数对FGM梁固有振动特性的影响.结果表明,剪切变形不仅会影响弯曲振动,对轴向振动也有影响.

Free Vibration Analysis of Functionally Graded Timoshenko Beams with Variable Section

Based on the concept of physical neutral surface, the governing differential equations of free vibration of an axial-loaded functionally graded material (FGM) beam with the material properties varying along the beam height are derived by using Hamilton principle, and then the power series solutions of the differential equations are obtained. Then, the frequency equation is obtained based on the general boundary conditions expressed by elastic constraints. The effects of the parameters such as the length-height ratio, the gradient index, the axial force, and the section variation coefficient on the natural vibration characteristics of functionally graded beams are analyzed. The results show that the shear deformation affects not only the flexural vibration but also the axial vibration.