On Parametric Instability Boundaries of Axially Moving Beams with Internal Resonance

作     者：You-Qi Tang Yuan-Xun Zhang Xiao-Dong Yang 

作者机构：School of Mechanical Engineering Shanghai Institute of Technology Shanghai 201418 China Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering College of Mechanical Engineering Beijing University of Technology Beijing 100124 China 

出 版 物：《Acta Mechanica Solida Sinica》 (固体力学学报（英文版）)

年 卷 期：2018年第31卷第4期

页      面：470-483页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 081304[工学-建筑技术科学] 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] 0813[工学-建筑学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：This work was supported by the National Natural Science Foundation of China (Project No. 11672186  11672007  11502147  11602146)  the Chen Guang Project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (No. 14CG57)  the training scheme for the Youth Teachers of Higher Education of Shanghai (No. ZZyyy12035)  and the Alliance Program (No.LM201663) 

主　　题：Parametric stability Axially moving beam Instability boundary Modal interac-tions 

摘      要：In this paper, the instability boundaries of an axially moving viscoelastic beam due to parametric resonance are revisited for the internal resonance case. The relation between the time-dependent tension and the time-dependent axial speed is constructed, which provides a new model in the study of axially moving material with pulsation parameters. The instability boundaries caused by the combination of parametric and internal resonances are studied using the method of multiple time scales. Some strange instability boundaries are detected when the internal resonance is considered. The phenomenon of local zigzag boundary contour is explained from the viewpoint of modal interactions.