Period-one rotating solution of parametric pendulums by iterative harmonic balance

Abstract

In this study, an iterative method based on harmonic balance for the period-one rotation of parametrically excited pendulum is proposed. Based on the characteristics of the period-one rotating orbit, the exact form of the solution is represented using the Fourier series. An iterative harmonic balance process is proposed to estimate the coefficients in the exact solution form. The general formula for each iteration step is presented. The bounds of excitations required for period-one rotations and the convergence of the method are investigated. The method is evaluated using two performance indexes, i.e. system energy error and global residual error. The performance of the proposed method is compared with the existing perturbation method. The numerical results obtained from MATLAB© are used as the baseline of the evaluation.