摘要
为研究不同高阶剪切变形理论下功能梯度梁的自由振动问题,假设功能梯度梁的材料参数按照组分的体积分数梯度变化,由哈密顿原理导出Winkler弹性地基上的功能梯度梁自由振动问题的运动方程.根据微分求积法原理,给出了考虑高阶剪切变形的功能梯度梁自由振动离散化代数方程.数值计算结果分析与讨论,研究了不同边界条件、弹性地基参数、功能梯度指数和结构几何参数对功能梯度梁固有频率的影响规律.该问题的研究可为功能梯度梁的设计与优化提供理论参考.
In order to study the free vibration problem of functionally graded beams for different high-order shear-deformed beam theories,it is assumed that the material properties of the functionally graded beam vary according to the gradient distribution of the volume fraction of the components.The equations of motion of functionally graded beams rested on the Winkler elastic foundation are derived from the principle of Hamiltonian.Based on the basic principle of DQM,the discretization equation for the free vibration of high-order shear deformed beams is presented.The effect of different boundary conditions,foundation coefficient,gradient index and geometric parameters on the free vibration of functionally graded beams are discussed through the numerical results.The study of this problem can provide a theoretical reference to the design and optimization of functionally graded beams.
作者
吴明明
李艳松
WU Mingming;LI Yansong(College of Civil Engineering,Hebei University of Engineering,Handan 056038,China)
出处
《辽宁工程技术大学学报（自然科学版）》
CAS
北大核心
2019年第5期424-429,共6页
Journal of Liaoning Technical University (Natural Science)
基金
河北省自然科学基金(A2018402158)
河北省引进留学人员资助项目(C201805).
关键词
功能梯度梁
高阶梁理论
微分求积法
自由振动
弹性地基
functionally graded beam
higher-order beam theory
differential quadrature method
free vibration
elastic foundation
