弹性地基上受压矩形纳米板的自由振动与屈曲特性  

Free vibration and buckling characteristics of compressed rectangular nanoplates resting on elastic foundation

作　　者：滕兆春[1] 刘露 衡亚洲 TENG Zhaochun;LIU Lu;HENG Yazhou(School of Science,Lanzhou University of Technology,Lanzhou 730050,China;Jiangsu Xingda Steel Cord Co.,Ltd.,Xinghua 225721,China)

机构地区：[1]兰州理工大学理学院,兰州730050 [2]江苏兴达钢帘线股份有限公司,江苏兴化225721

出　　处：《振动与冲击》2019年第16期208-216,232,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(11662008)

摘　　要：基于Eringen非局部弹性理论和经典薄板理论,利用Hamilton原理推导Winkler-Pasternak弹性地基上面内受压正交各向异性矩形纳米板自由振动的控制微分方程并进行无量纲化。采用一种半解析方法—微分变换法(DTM)将无量纲控制微分方程及边界条件变换为等价的代数方程,得到含有无量纲固有频率和屈曲载荷的特征方程。数值给出了不同边界条件下无量纲地基刚度系数、压力强度、载荷参数、长宽比和纳米尺度对正交各向异性矩形纳米板无量纲固有频率的影响以及不同无量纲地基刚度系数、载荷参数和纳米尺度下的屈曲临界载荷值。结果表明:正交各向异性矩形纳米板的无量纲固有频率随无量纲地基刚度系数、载荷参数和长宽比的增大而增大,随纳米尺度的增大而趋向减小;屈曲临界载荷也随无量纲地基刚度系数的增大而增大,随纳米尺度的增大而减小。Based on the Eringen’s nonlocal elasticity theory and the classical thin plate theory,the governing differential equation for free vibration of in-plane compressed orthotropic nanoplate resting on Winkler-Pasternak elastic foundation was derived by using the Hamilton’s principle.Then the dimensionless form of the governing differential equation was also obtained.The dimensionless governing differential equation and boundary conditions were transformed to the equivalent algebraic equations by using a semi-analytic method called differential transformation method(DTM),which can derive characteristic equations of dimensionless natural frequencies and buckling loads.The influence of dimensionless foundation stiffness coefficients,pressure intensity,load parameter,aspect ratio and nano-scale factor on the dimensionless natural frequency of orthotropic rectangular nanoplate under different boundary conditions was numerically presented and the critical buckling load values of different dimensionless foundation stiffness coefficients,load parameter and nano-scale factor were given.The results show that the dimensionless natural frequency of orthotropic rectangular nanoplate increases with dimensionless foundation stiffness coefficients,load parameter and aspect ratio;decreases with nano-scale factor.The critical buckling load increases with dimensionless foundation stiffness coefficient,decreases with nano-scale factor.

关 键 词：Eringen非局部弹性理论 Winkler-Pasternak弹性地基 无量纲固有频率 屈曲临界载荷 微分变换法(DTM) 

分 类 号：O343[理学—固体力学]