Nonlinear Dynamics

, Volume 70, Issue 4, pp 2433–2444

# Iterative harmonic balance for period-one rotating solution of parametric pendulum

Original Paper

## 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 definition of the period-one rotating orbit, the exact form of the solution can be obtained 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 method is evaluated using two criteria, which are the system energy error and the global residual error. The performance of the proposed method is compared with the results from multiscale method and perturbation method. The numerical results obtained with the Dormand–Prince method (ODE45 in MATLAB©) are used as the baseline of the evaluation.

## Keywords

Parametric pendulum Iteration Rotating orbits Harmonic balance Nonlinear systems

## Notes

### Acknowledgements

The advice and guidance provided by Dr. S.C. Liu, Program Director, are gratefully acknowledged.

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