一般边界条件下功能梯度梁三维振动特性研究  

Three-dimensional vibration analysis of FGM beams with general boundary conditions

作　　者：陈玉坤 靳国永[1] 叶天贵 CHEN Yu-kun;JIN Guo-yong;YE Tian-gui(College of Power and Energy Engineering,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨工程大学动力与能源工程学院,黑龙江哈尔滨150001

出　　处：《振动工程学报》2020年第4期756-763,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51709066,51775125);中国博士后科学基金资助项目(2018T110277,2017M621252);黑龙江省自然科学基金资助项目(QC2018058);中央高校基本科研业务费专项资金——博士研究生科研创新基金资助项目(3072019GIP0303)。

摘　　要：基于卡莱拉统一公式(CUF)建立了一般边界条件下功能梯度(FGM)梁的高阶统一动力学模型和分析方法。利用二维泰勒公式对FGM梁截面位移函数进行高阶拟合,经典梁理论可以视为一阶泰勒公式的特殊形式。采用Voigt线性混合模型分别考虑了两种功能梯度材料分布形式:材料属性仅沿宽度或厚度单一方向发生变化;材料属性同时沿宽度和厚度方向发生变化。通过罚函数法将FGM梁的边界条件量化为边界能量的形式,实现了对边界条件的参数化分析,并消除了位移容许函数对边界条件的依赖性。利用瑞利-利兹法和勒让德多项式函数对FGM梁的振动问题进行求解。通过与文献中结果对比,验证了此方法的有效性和正确性。最后,研究了几何尺寸、材料属性和边界条件对FGM梁振动特性的影响规律。In this study,a uniform dynamic model is established using Carrera unified formulation for the vibration analysis of FGM beams with general boundary conditions.Higher-order Taylor expansions are used to simulate the cross-sectional displacement functions,and the classical beam theories can be seen as particular cases of the first-order Taylor expansion.Two types of material distribution over the beam’s cross-section are considered by utilizing the Voigt model and power-law function.The penalty method is applied and three groups of penalty factor are used for the boundary conditions of the FGM beam.In this way,the energy stored in the boundary conditions can be considered as a part of the total energy function,releasing the limitation of geometrical boundary restraints on the selection of admissible functions.The Rayleigh-Ritz method and Legendre polynomial functions are utilized to address the vibration problem of the FGM beams.Several numerical examples are carried out to demonstrate the effectiveness and correctness of the present method.Finally,the effects of the geometrical dimensions,material parameters and boundary conditions on the vibration characteristics of the FGM beams are studied.

关 键 词：结构振动 功能梯度梁 一般边界条件 卡莱拉统一公式(CUF) 罚函数方法 

分 类 号：O327[理学—一般力学与力学基础] O326[理学—力学]