弹性地基上含孔隙功能梯度材料板的自由振动和动力响应  

Free vibration and dynamic response of porous functionally graded plates on elastic foundation

作　　者：黄小林 董雷 钟德月 魏耿忠 Huang Xiaolin;Dong Lei;Zhong Deyue;Wei Gengzhong(School of Architecture and Transportation Engineering,Guilin University of Electronic Technology,541004,Guilin,China)

机构地区：[1]桂林电子科技大学建筑与交通工程学院,桂林541004

出　　处：《应用力学学报》2021年第1期402-408,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11362004);桂林电子科技大学研究生教育创新计划资助项目(2019YCXS118)。

摘　　要：为研究弹性地基上含孔隙的材料特性沿厚度呈Sigmoid函数变化的功能梯度材料(S-FGM)板的振动特性,本文基于改进的Voigt模型,分别建立了孔隙为均匀分布和非均匀分布两种类型的功能梯度材料的物性参数模型。根据复合材料薄板理论导出了弹性地基上含孔隙的功能梯度材料板的运动方程,用伽辽金法寻求四边简支边界条件下板自由振动和动力响应的解析解;讨论了孔隙、弹性地基参数、材料组分指数等因素对S-FGM板自由振动和动力响应的影响。结果表明:孔隙对板自振频率的影响比较复杂,不仅与孔隙率的大小和分布形式有关,还与弹性地基参数有关;当有弹性地基作用时,板的量纲归一化基频随着孔隙率的增大而提高,并且孔隙均匀分布的S-FGM板与孔隙非均匀分布的情况相比,其量纲归一化基频更高;孔隙增大了板的动力响应,其中孔隙为均匀分布的板的动力响应对孔隙率的变化更为敏感。This paper focuses on the vibrational characteristics of porpous sigmoid functionally graded material(S-FGM) plates on elastic foundations. Based on an improved Voigt model, the effective material properties of the plates with evenly and unevenly distributed porosities are estimated. According to the composite thin plate theory, the equations of motion for the plates on elastic foundations are derived. The analytical solution for the free vibrations and dynamic responses of the simply supported plates are obtained by using Galerkin method. The effects of the pore volume fraction, elastic foundation parameters, and power law index on the natural frequencies and dynamic responses of the plate are investigated. The results show that the influence of pores on the natural frequencies is complicated and which relates to the changes of the pores and foundation parameters. The natural frequency of the plates on elastic foundation rises with the increase of porosity volume fraction. The natural frequencies of S-FGM plates with evenly distributed porosities are higher than those with unevenly distributed porosities. The peak dynamic responses increase as porosity volume fraction rises. Compared with the uneven distribution, the dynamic responses with the even distribution are more sensitive to the change of porosity volume fraction.

关 键 词：功能梯度材料 孔隙 弹性地基 振动 

分 类 号：O327[理学—一般力学与力学基础]