Stationary Vibration Analysis of Time-Periodic Systems via a Wavelet-Based Searching Procedure
Résumé
A Wavelet-Galerkin procedure was introduced in a previous paper to exhibit the transient response of parametrically excited systems involving both irregular time-varying coefficients and a relatively large number of degrees of freedom. The main scope of the present study is to introduce a wavelet technique allowing to seek periodic orbits of such dynamical systems and the associated periodic initial conditions. A few academic instances including a 1 dof Mathieu oscillator and a 3-dof system illustrate the relevance of the method by comparison with well established numerical techniques such as Runge-Kutta for example. Prospective researches are finally set to extend the wavelet method to the nonlinear case.