功能梯度多孔磁电弹板的等几何建模与自由振动分析  

Iso-geometric modeling and free vibration analysis of FGP-MEE plates

作　　者：刘庆运[1] 张红一 白凯凯 胡晓磊[1] 刘涛[1] LIU Qingyun;ZHANG Hongyi;BAI Kaikai;HU Xiaolei;LIU Tao(School of Mechanical Engineering,Anhui University of Techology,Ma’anshan 243002,China)

机构地区：[1]安徽工业大学机械工程学院,安徽马鞍山243002

出　　处：《振动与冲击》2024年第15期169-178,共10页Journal of Vibration and Shock

基　　金：安徽省高校自然科学研究重点项目(KJ2021A0404,KJ2021A0368)。

摘　　要：针对功能梯度多孔磁电弹(functional graded porous-magneto electro elastic,FGP-MEE)板结构,该文基于等几何分析法(isogeometric analysis,IGA),采用一阶剪切变形理论(first-order shear deformation theory,FSDT)建立了等几何数值分析模型。首先,根据修正幂律(modified power law,MPL)方法得到了具有4种不同孔隙分布形式(V_(u),V_(o),V_(x),V_(v))功能梯度多孔磁电弹结构的等效材料参数;然后,利用磁-电-弹耦合本构方程、哈密顿变分原理以及等几何分析方法推导了FGP-MEE板的控制方程,并通过与已有文献对比,验证了所建模型的有效性和准确性;最后,研究了孔隙系数、功能梯度指数、孔隙分布形式、结构的几何参数(宽厚比、长宽比)以及边界条件对FGP-MEE板自由振动的影响。研究结果表明,材料中孔隙分布形式、孔隙系数以及功能梯度指数的变化对FGP-MEE板的固有频率有较大影响,且在孔隙呈V_o型分布时板的固有频率最大。Here,aiming at functionally graded porous magneto-electro-elastic(FGP-MEE)plate structures,based on the iso-geometric analysis method(IGA),the iso-geometric numerical analysis model was established using the first-order shear deformation theory(FSDT).Firstly,equivalent material parameters of FGP-MEE structures with 4 different pore distribution forms of V_(u),V_(o),V_(x)and V_(v)were obtained using the modified power law(MPL)method.Then,the governing equation of motion for FGP-MEE plate was derived using the magneto-electro-elastic coupled constitutive equation,Hamiltonian variational principle and IGA method.The effectiveness and correctness of the established model were verified by comparing it with existing literature published.Finally,effects of pore coefficient,functional gradient index,pore distribution form,geometric parameters of structure including width-thickness ratio,length-width ratio and boundary conditions on free vibration of FGP-MEE plate were studied.The study results showed that changes of pore distribution form,pore coefficient and functional gradient index in material affect natural frequencies of FGP-MEE plate more largely;natural frequencies of the plate with pore distribution form of V o are maximum.

关 键 词：功能梯度多孔磁电弹(FGP-MEE)板 等几何分析法(IGA) 一阶剪切变形理论(FSDT) 自由振动 

分 类 号：O343[理学—固体力学]