Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory  

作　　者：Shaowu YANG Yuxin HAO Wei ZHANG Li YANG Lingtao LIU 

机构地区：[1]College of Mechanical Engineering,Beijing Information Science and Technology University,Beijing 100192,China [2]Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures,College of Mechanical Engineering,Beijing University of Technology,Beijing 100124,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2021年第7期981-998,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12002057,11872127,11832002);the Scientific Research Project of Beijing Educational Committee(No.KM202111232023);the Qin Xin Talents Cultivation Program,Beijing Information Science&Technology University(Nos.QXTCP C202102,A201901)。

摘　　要：In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vibration analyses of the FG-GPLRC truncated conical shell are presented.Considering the graphene platelets(GPLs)of the FG-GPLRC truncated conical shell with three different distribution patterns,the modified Halpin-Tsai model is used to calculate the effective Young’s modulus.Hamilton’s principle,the FSDT,and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell.The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell.Then,the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method.The effects of the weight fraction and distribution pattern of the GPLs,the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed.This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.

关 键 词：nonlinear free vibration harmonic balance method functionally graded graphene platelet-reinforced composite(FG-GPLRC) truncated conical shell chaos 

分 类 号：O322[理学—一般力学与力学基础]