Stationary vibration analysis of time-periodic systems via a wavelet-based searching procedure

Authors:
C.-H. Lamarque;S. Pernot
Affiliations:
Ecole Nationale des Travaux Publics de l'Etat, Laboratoire GéoMatériaux, URA-CNRS 1652, 1 rue Maurice Audin, 69518 Vaulx-En-Velin Cedex, France;Ecole Nationale des Travaux Publics de l'Etat, Laboratoire GéoMatériaux, URA-CNRS 1652, 1 rue Maurice Audin, 69518 Vaulx-En-Velin Cedex, France
Venue:
Systems Analysis Modelling Simulation
Year:
2002

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Abstract

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.