TY - GEN
T1 - Study on strongly odd nonlinear oscillations by means of the homotopy analysis method
AU - Jianmin, Wen
AU - Bindi, You
AU - Xinzhi, Han
AU - Yumeng, Li
PY - 2013
Y1 - 2013
N2 - An analytical technique, namely the homotopy analysis method (HAM), is applied to solve periodic solutions for free oscillations with strongly odd nonlinearities of 5 degree polynomials. Unlike perturbation methods such as the method of multiple scales which must depend on a small parameter, HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniques, the HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter h. In this paper, periodic analytic approximations for free oscillations with odd nonlinearities of degree 5 polynomials are obtained by using the HAM for the first time, which agree well with numerical results. This article shows that the HAM is a powerful and effective technique for nonlinear dynamical systems.
AB - An analytical technique, namely the homotopy analysis method (HAM), is applied to solve periodic solutions for free oscillations with strongly odd nonlinearities of 5 degree polynomials. Unlike perturbation methods such as the method of multiple scales which must depend on a small parameter, HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniques, the HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter h. In this paper, periodic analytic approximations for free oscillations with odd nonlinearities of degree 5 polynomials are obtained by using the HAM for the first time, which agree well with numerical results. This article shows that the HAM is a powerful and effective technique for nonlinear dynamical systems.
UR - https://www.scopus.com/pages/publications/84882427167
U2 - 10.1109/ICCA.2013.6565135
DO - 10.1109/ICCA.2013.6565135
M3 - 会议稿件
AN - SCOPUS:84882427167
SN - 9781467347075
T3 - IEEE International Conference on Control and Automation, ICCA
SP - 918
EP - 922
BT - 2013 10th IEEE International Conference on Control and Automation, ICCA 2013
T2 - 2013 10th IEEE International Conference on Control and Automation, ICCA 2013
Y2 - 12 June 2013 through 14 June 2013
ER -