文献类型：期刊文献

英文题名：Vibration of axially moving hyperelastic beam with finite deformation

作者：Wang, Yuanbin[1,2];Ding, Hu[2];Chen, Li-Qun[3]

机构：[1]ShaoXing Univ, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China;[2]Shanghai Univ, Shanghai Key Lab Mech Energy Engn, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China;[3]Harbin Inst Technol, Sch Sci, Shenzhen 518055, Peoples R China

年份：2019

卷号：71

起止页码：269

外文期刊名：APPLIED MATHEMATICAL MODELLING

收录：SCI-EXPANDED(收录号：WOS:000468259900016)、、EI(收录号：20190906560818)、Scopus(收录号：2-s2.0-85062025691)、WOS

基金：This project was supported by the Natural Science Foundation of China [nos.11872159, 11572182, 11422214 and 11472177] and the Natural Science Foundation of Zhejiang Province [no. LY19A020005]

语种：英文

外文关键词：Hyperelastic beam; Critical velocity; Shear deformation theory; Natural frequency

外文摘要：In this paper, we study the vibration of an axially moving hyperelastic beam under simply supported condition. The kinematic of the axially moving beam have been described by Eulerian-Lagrangian formulation. In continuum mechanics frame, the finite deformation formula and a higher order shear deformation beam theory are applied to describe the deformation of the axially moving hyperelastic beam. In these formulas the material parameter, shear deformation and the geometric non-linearity have been taken into account. Through the Hamilton principle, the governing equations of nonlinear vibration are obtained, where the transverse vibration is coupled with the longitudinal vibration. When the velocity is a constant, the critical speed and natural frequencies are determined by solving the corresponding linear equations. Meantime, effects of the geometrical and material parameters on the critical speed and natural frequencies have been investigated. Comparisons among the critical velocities of the hyperelastic and Euler linear beam are also made. The results show that the critical velocity of hyperelastic beam is larger than that of linear Euler-Bernoulli beam. For the natural frequencies, we have the same conclusions. Lastly, by the multiple scales method, the leading order analytical solutions of the equilibrium state of axially moving hyperelastic beam in the supercritical regime are obtained. Furthermore the amplitudes of analytical solutions of the hyperelastic beam have been compared with that of linear Euler-Bernoulli beam. The effects of the material and geometrical parameters on the asymptotic solutions and the amplitude has been analyzed. (C) 2019 Elsevier Inc. All rights reserved.