A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

作     者：Lu LU Li ZHU Xingming GUO Jianzhong ZHAO Guanzhong LIU 

作者机构：Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering School of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072 China Department of Mechanical Engineering University of Alberta School of Mathematics and Computational Sciences Xiangtan UniversityXiangtan 411105 Hunan Province China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2019年第40卷第12期

页      面：1695-1722页

核心收录：

学科分类：08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 080102[工学-固体力学] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11872233 and11472163) the China Scholarship Council(No.201706890041) the Innovation Program of Shanghai Municipal Education Commission(No.2017-01-07-00-09-E00019) 

主　　题：nonlocal strain gradient theory surface elasticity theory rst-order shear deformation theory vibration functionally graded (FG) cylindrical nanoshell 

摘      要：In this pap er, a novel size-dep endent functionally graded (FG) cylindrical shell model is develop ed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory . The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical typ es of size e ects simultaneously , which are the nonlocal stress ef- fect, the strain gradient e ect, and the surface energy e ects. With the help of Hamilton’s principle and rst-order shear deformation theory , the non-classical governing equations and related b oundary conditions are derived. By using the prop osed model, the free vibra- tion problem of FG cylindrical nanoshells with material prop erties varying continuously through the thickness according to a p ower-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various b oundary conditions are obtained. After verifying the reliability of the prop osed model and analytical method by comparing the degenerated results with those available in the literature, the in uences of nonlocal parameter, material length scale parameter, p ower-law index, radius-to-thickness ratio, length-to-radius ratio, and surface e ects on the vibration characteristic of func- tionally graded cylindrical nanoshells are examined in detail.