Period-One Rotating Solutions of Horizontally Excited Pendulum Based on Iterative Harmonic Balance

Tian-Wei  Ma; Hui  Zhang

doi:10.4236/apm.2015.58041

Hui Zhang^*, Tian-Wei Ma

Abstract: In this study, the iterative harmonic balance method was used to develop analytical solutions of period-one rotations of a pendulum driven horizontally by harmonic excitations. The performance of the method was evaluated by two criteria, one based on the system energy error and the other based on the global residual error. As a comparison, analytical solutions based on the multi-scale method were also considered. Numerical solutions obtained from the Dormand-Prince method (ODE45 in MATLAB©) were used as the baseline for evaluation. It was found that under lower-level excitations, the multi-scale method performed better than the iterative method. At higher-level excitations, however, the performance of the iterative method was noticeably more accurate.

Keywords: Iterative Harmonic Balance, Period-One Rotation, Horizontal Pendulum, Nonlinear System

Cite this paper: Zhang, H. and Ma, T. (2015) Period-One Rotating Solutions of Horizontally Excited Pendulum Based on Iterative Harmonic Balance. Advances in Pure Mathematics, 5, 413-427. doi: 10.4236/apm.2015.58041.

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