Sub-Harmonic Resonances of Periodic Parameter Excited Oscillators with Discontinuities

作     者：Jifeng Cui 

作者机构：School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong University 

出 版 物：《Journal of Harbin Institute of Technology(New Series)》 (哈尔滨工业大学学报（英文版）)

年 卷 期：2015年第22卷第4期

页      面：66-71页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 080101[工学-一般力学与力学基础] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Sponsored by the National Natural Science Foundation of China(Grant No.11272209) the State Key Laboratory of Ocean Engineering(Grant No.GKZD010059) 

主　　题：periodic parameter excited oscillator sub-harmonic resonance HAM Fourier expansion 

摘      要：It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.