Modeling and analysis of an inextensible beam with inertial and geometric nonlinearities  

作　　者：Zhanhuan YAO Tieding GUO Wanzhi QIAO 

机构地区：[1]College of Civil and Architecture Engineering,Guangxi University,Nanning 530005,China [2]School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China [3]School of Civil and Environment Engineering,Harbin Institute of Technology,Shenzhen,Shenzhen 518000,Guangdong Province,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第12期2113-2130,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.12372007,12432001,12372006,and 11972151)。

摘　　要：The present study focuses on an inextensible beam and its relevant inertia nonlinearity,which are essentially distinct from the commonly treated extensible beam that is dominated by the geometric nonlinearity.Explicitly,by considering a weakly constrained or free end(in the longitudinal direction),the inextensibility assumption and inertial nonlinearity(with and without an initial curvature)are introduced.For a straight beam,a multi-scale analysis of hardening/softening dynamics reveals the effects of the end stiffness/mass.Extending the straight scenario,a refined inextensible curved beam model is further proposed,accounting for both its inertial nonlinearity and geometric nonlinearity induced by the initial curvature.The numerical results for the frequency responses are also presented to illustrate the dynamic effects of the initial curvature and axial constraint,i.e.,the end mass and end stiffness.

关 键 词：inextensible beam inertia nonlinearity initial curvature geometric nonlinearity hardening/softening dynamics 

分 类 号：O322[理学—一般力学与力学基础]