纳米多层各向同性弹性球壳的轴对称自由振动  

Axisymmetric Free Vibration of Nano-sized Multi-layered Isotropic Elastic Spherical Shells

作　　者：李雄俊 熊慧芳[2] 肖潭 LI Xiongjun;XIONG Huifang;XIAO Tan(School of Architectural and Civil Engineering,Guangdong University of Petrochemical Technology,Maoming 525000,China;Modern Educational Technology Center,Guangdong University of Petrochemical Technology,Maoming 525000,China)

机构地区：[1]广东石油化工学院建筑工程学院,广东茂名525000 [2]广东石油化工学院现代教育技术中心,广东茂名525000

出　　处：《广东石油化工学院学报》2024年第4期114-120,共7页Journal of Guangdong University of Petrochemical Technology

基　　金：广东省基础与应用基础研究基金项目(2020A1515011241)。

摘　　要：经典连续体力学理论不再适用于具有尺度效应的微纳结构问题求解。运用状态空间方法和非局域弹性理论,建立考虑非局域效应的纳米多层球壳模型,求解了纳米多层球壳的轴对称自由振动问题。分别以不同半径的银、金纳米粒子为例进行计算并与低频拉曼散射实验值进行比较。研究结果表明:取纳米粒子的半径为材料的内特征尺度,各粒子结构自由振动频率的计算值与实验值基本相符。上述力学模型有望应用于超声作用下纳米靶向超声造影剂振动分析或其他纳米多层壳结构振动分析等。The classical continuum mechanics is inapplicable to those size-dependent problems of micro/nano structures.A size-dependent nano-sized multi-layered spherical shell model is built for solving vibration problems of nano-sized multi-layered spherical shells,and the axisymmetric free vibration problem of the shell has been solved by using state-space method and nonlocal elasticity theory.The silver and gold nanoparticles of three radius cases have been used as computation examples and the computation outcomes are compared with those of low frequency Raman scattering experiments.The results show that the computational values of the free vibration frequency of the nanoparticles are in good agreement with experimental ones,providing that the radius of the nano-sized particles was used as the internal characteristic length of the material.It is promising that the above-mentioned mechanical model is applicable for vibration analysis of nano targeted ultrasound contrast agent or of other nano-sized multi-layered shell structures.

关 键 词：多层球壳 尺度效应 轴对称振动 非局域弹性理论 各向同性弹性 

分 类 号：O343[理学—固体力学]