压电/压磁双层纳米板的振动特性  

Vibration properties of piezoelectric/piezomagnetic bilayer nanoplates

作　　者：温建俊 张乐乐 刘金喜 WEN Jianjun;ZHANG Lele;LIU Jinxi(School of Civil Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Hebei Research Center of the Basic Discipline Engineering Mechanics,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学土木工程学院,河北石家庄050043 [2]河北省工程力学基础学科研究中心,河北石家庄050043

出　　处：《哈尔滨工程大学学报》2025年第2期227-233,共7页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(11802185);河北省自然科学基金项目(A2019210203,A2023210064);河北省教育厅科学研究项目(BJK2022055)。

摘　　要：为了获得微纳米磁电层合结构的振动力学性能,本文以压电/压磁双层纳米板为研究对象。在压电层和压磁层中独立假设位移和电磁场量,令其满足界面处位移和剪应力连续条件,以及表面应力自由条件;引入非局部压电/压磁本构关系表征尺度效应,基于Hamilton原理建立了纳米压电/压磁双层板的振动控制方程;利用Navier解获得了结构在四边简支情形下的固有频率,并通过算例详细讨论了非局部参数、结构尺寸、外加机械荷载等因素对振动特性的影响。研究表明:非局部效应会显著改变压电/压磁双层板的固有频率,随着非局部参数的增大,固有频率会随之减小。本文结论可为微纳米磁电层合结构的动力学性能优化提供理论支撑。The free vibration properties of a nanoscale piezoelectric-piezomagnetic bilayer plate are investigated,considering the piezoelectric/piezomagnetic bilayer nanometer plate as the research object.First,a displacement and an electromagnetic field volume were independently assumed;such values shall satisfy the conditions of continual displacement and shear stress at the interface,as well as the condition of free surface stress.Second,by introducing nonlocal piezoelectric/piezomagnetic constitutive relations for characterizing the scale effects,the vibration governing equations of the piezoelectric/piezomagnetic bilayer nanoplate were derived on the basis of the Hamilton principle.Finally,the natural frequency of the bilayer plate simply supported at all edges was obtained using the Navier solution,and the numerical examples were provided to discuss the impact of nonlocal parameters,structure size,and external load upon the vibration characteristics in detail.Analysis results show that the nonlocal effects may considerably change the natural frequency of the piezoelectric/piezomagnetic bilayer plate,and the natural frequency decreases with the increase in nonlocal parameters.This study can provide theoretical support for the dynamic performance optimization of micro-nano magnetic/electric laminating structures.

关 键 词：层状复合材料 压电材料 压磁材料 双层板 纳米尺度 非局部理论 机械荷载 振动特性 

分 类 号：O326[理学—一般力学与力学基础] O343.1[理学—力学]