Dynamic quasi-continuum model for plate-type nano-materials and analysis of fundamental frequency  

作　　者：Chunxiao XIA Wenlong XU Guohua NIE 

机构地区：[1]School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2021年第1期85-94,共10页应用数学和力学（英文版）

摘　　要：A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components and angles of rotations are given.As an application of the model,the cylindrical bending deformation of the structure fixed at two ends is analyzed,and a theoretical formula evaluating the fundamental frequency is obtained by using Galerkin's method.Meanwhile,the solution for the classical continuous plate model is also derived,and the size-dependent elastic modulus and Poisson's ratio are taken in computation.The frequencies corresponding to different atomic layers are numerically presented for the plate-type NaC l nano-materials.Furthermore,a molecular dynamics(MD)simulation is conducted with the code LAMMPS.The comparison shows that the present quasi-continuum model is valid,and it may be used as an alternative model,which reflects scale effects in analyzing dynamic behaviors of such plate-type nano-materials.

关 键 词：plate-type nano-material quasi-continuum model SIZE-DEPENDENT fundamental frequency theoretical solution molecular dynamics(MD)simulation 

分 类 号：O302[理学—力学] O327