Invariant and energy analysis of an axially retracting beam

作     者：Yang Xiaodong Liu Ming Zhang Wei Roderick V.N.Melnik 

作者机构：Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering College of Mechanical Engineering Beijing University of Technology M2NeT Laboratory The MS2Discovery Interdisciplinary Research Institute Wilfrid Laurier University 

出 版 物：《Chinese Journal of Aeronautics》 (中国航空学报（英文版）)

年 卷 期：2016年第29卷第4期

页      面：952-961页

核心收录：

学科分类：08[工学] 0825[工学-航空宇航科学与技术] 

基　　金：supported by the National Natural Science Foundation of China (Nos. 11322214, 11172010, 11290152 and 11402007) supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Canada Research Chair (CRC) Program the Bizkaia Talent Grant under the Basque Government through the BERC 2014–2017 Program Spanish Ministry of Economy and Competitiveness MINECO:BCAM Severo Ochoa excellence accreditation SEV-2013-0323 

主　　题：Adiabatic invariants Asymptotic analysis Retracting beam Time-varying systems Transient dynamics 

摘      要：The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem. The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations (ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retraction. The total energy varying with time has been investigated by numerical and analytical methods, and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.