轴向功能梯度变截面梁的自由振动研究  

FREE VIBRATION OF AXIALLY FUNCTIONALLY GRADED BEAMS WITH NON-UNIFORM CROSS-SECTION

作　　者：汪亚运[1] 彭旭龙[1] 陈得良[1] 

机构地区：[1]长沙理工大学土木与建筑学院,长沙410004

出　　处：《固体力学学报》2015年第5期384-391,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金资助项目(11202038;11172051);湖南省自然科学基金项目(2015JJ4006);湖南省教育厅资助科研项目(13C1031;YB2012B032);长沙理工大学桥梁工程湖南省高校重点实验室开放基金项目(13KC02)资助

摘　　要：论文引入一种新的、简单易行的近似方法,求解轴向非均匀变截面梁的自由振动固有频率.将位移展开成切比雪夫多项式,从而变系数控制微分方程转化为含未知系数的齐次线性方程组.利用非零解的存在条件,进而得到含固有频率的特征方程.通过和特定梯度下已有的精确解进行比较,验证了该方法的精度和有效性,并分析了梯度参数、支承条件等对固有频率的影响.A new and simple approximate method is introduced to solve natural frequencies of free vibration of beams with axially inhomogeneity in this paper.The governing differential equation is transformed to a system of linear algebraic equations by changing the form of the expression of displacement with the Chebyshev polynomials expansion.Under the non-zero solution of existence conditions,the characteristic equations are numerically obtained to get the natural frequency.The effectiveness and accuracy of present method are confirmed by comparing numerical results with the exact solution of some specific gradient.Furthermore,the influences of gradient parameter and support conditions on natural frequency are studied.

关 键 词：功能梯度材料 切比雪夫多项式 欧拉-伯努利梁 自由振动 固有频率 

分 类 号：O327[理学—一般力学与力学基础]