Forced Response Approach to Predict Parametric Vibration.

In this paper, forecast modelling based on modulation feedback is used to investigate the forced response of parametric vibration with a damper. The system is excited by both the periodic coefficient and external force terms, which have different periods. In this study, the forced response is expressed as a linear combination of harmonic components. By applying harmonic balance, the parametric equation is converted into a set of infinite-order linear algebraic equations. Then, by taking the limit to infinity, all coefficients of the harmonic components in the forced response are fully expanded into a series. The advantages of the presented approach are (1) the forced response expressed as a trigonometric series is easier to apply in practice and (2) all coefficients of the harmonic components can be determined by numerical computation. The accuracy of the proposed approach has been verified by comparing resulting phase diagram trajectories with those obtained by the standard Runge-Kutta method. The results show that the presented approach is suitable for the forced response approach and the nonlinear characterization of parametric vibration. [ABSTRACT FROM AUTHOR]