基于能量有限元法的功能梯度梁振动分析

摘要

功能梯度材料(Functionally Graded Material,FGM)由于其优良的结构性能和重要的应用价值,近些年来得到了广泛的研究和关注.采用能量有限元法对功能梯度梁和耦合梁的弯曲振动特性进行研究,推导了功能梯度材料梁的能量密度控制方程、能量有限元矩阵方程以及耦合梁的能量有限元方程,从而得到梁中的能量密度和能量流.以一简支功能梯度梁为例,分别采用该方法和传统有限元法计算了梁弯曲振动时的能量密度,通过对比验证了能量有限元法求解的准确性.在此基础上进一步对耦合功能梯度梁结构的能量密度和能量流进行了求解,得到其能量分布特征.该研究为基于能量有限元法分析复杂功能梯度材料结构的振动特性提供了理论基础.%Functionally graded materials (FGMs) are more and more widely used in engineering because of their excellent structural properties and important application value.Here,bending vibration characteristics of FGM beams and coupled beams were analyzed based on the energy finite element method.In order to get the energy density and energy flow,FGM beam energy density control equation and energy finite element matrix equation as well as coupled beam energy finite element matrix equation were deduced,respectively.Taking a simply supported FGM beam as an example,its energy density was computed with the energy finite element method and the traditional finite element method,respectively.The two energy densities were compared to verify the correctness of the proposed energy FE method.Then the energy density and energy flow of the coupled FGM beam were solved.Finally,the energy distribution features of the beam were obtained.This study provided a theoretical basis for the vibration characteristics analysis of complex FGM structures based on the energy finite element method.