计算力学学报2017，Vol.34Issue(6)：712-717,6.DOI:10.7511/jslx201706006
弹性地基上转动FGM梁自由振动的DTM分析
DTM analysis for free vibration of rotating FGM beams resting on elastic foundations
摘要
Abstract
Based on Euler-Bernoulli beam theory,the governing differential equation of motion of the lateral free vibration a rotating functionally graded material (FGM) beam on elastic foundation is derived by using generalized Hamilton principle,and differential transform method (DTM) is used to transform the dimensionless governing differential equation and the boundary conditions.At the same time,the dimensionless natural frequencies of transverse free vibration of rotating FGM beam on elastic foundation at the clamped-clamped,clamped-simply supported and clamped-free three boundary conditions are determined,then the governing differential equation is degenerated to the FGM without rotation and elastic foundation.The values of first non-dimensional natural frequency with different FGM gradient index are calculated and they are completely consistent with the results by either the FEM or the Lagrange multipliers method in the literature.The results show:at the above three kinds of the boundary conditions,the dimensionless natural frequencies increase with the growth of the dimensionless rotating speed and the dimensionless elastic foundation modulus.Under a certain dimensionless rotating speed and dimensionless elastic foundation modulus,the dimensionless natural frequencies decrease along with the growth of the FGM gradient index.However,when at clamped-simply supported and clamped-free boundary conditions,the first dimensionless natural frequency is almost constant.关键词
弹性地基/转动FGM梁/无量纲固有频率/广义Hamilton原理/微分变换法(DTM)Key words
elastic foundation/rotating FGM beam/non-dimensional natural frequency/generalized Hamilton principle/Differential Transform Method (DTM)分类
数理科学引用本文复制引用
滕兆春,衡亚洲,张会凯,马永斌..弹性地基上转动FGM梁自由振动的DTM分析[J].计算力学学报,2017,34(6):712-717,6.基金项目
国家自然科学基金(11662008)资助项目. （11662008）
