Nonlocal and strain gradient effects on nonlinear forced vibration of axially moving nanobeams under internal resonance conditions

作     者：Jing WANG Yilin ZHU Bo ZHANG Huoming SHEN Juan LIU Jing WANG;Yilin ZHU;Bo ZHANG;Huoming SHEN;Juan LIU

作者机构：School of Mechanical and Electrical EngineeringSouthwest Petroleum UniversityChengdu 610500China School of Civil Engineering and ArchitectureSouthwest Petroleum UniversityChengdu 610500China School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengdu 611756China Applied Mechanics and Structure Safety Key Laboratory of Sichuan ProvinceChengdu 611756China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2020年第41卷第2期

页      面：261-278页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11702036 11602204 and 11502218) 

主　　题：scale effect axially moving nanobeam internal resonance critical amplitude 

摘      要：Based on the nonlocal strain gradient theory(NSGT), a model is proposed for an axially moving nanobeam with two kinds of scale effects. The internal resonanceaccompanied fundamental harmonic response of the external excitation frequency in the vicinities of the first and second natural frequencies is studied by adopting the multivariate Lindstedt-Poincaré(L-P) method. Based on the root discriminant of the frequencyamplitude equation under internal resonance conditions, theoretical analyses are performed to investigate the scale effects of the resonance region and the critical external excitation amplitude. Numerical results show that the region of internal resonance is related to the amplitude of the external excitation. Particularly, the internal resonance disappears after a certain critical value of the external excitation amplitude is *** is also shown that the scale parameters, i.e., the nonlocal parameters and the material characteristic length parameters, respectively, reduce and increase the critical amplitude,leading to a promotion or suppression of the occurrence of internal resonance. In addition,the scale parameters affect the size of the enclosed loop of the bifurcated solution curves as well by changing their intersection, divergence, or tangency.