Décomposition en paquets d'ondes pour le calcul d'énergie vibratoire de structures

Abstract
At medium frequency range (MFR), numerous vibroacoustic problems deal with systems of large number of modes where classical modal methods must cope with resolution of huge linear system. In the idea of reducing theses models a mode hybridization method proposed in [1] gives one equivalent mode when modes of the complex structure are known. Another method [2],[4] based on reducing size of dynamic model in the MFR, gives a prediction of the vibration response of a structure by using a limited number of modes of the homogeneous master structure in order to interpolate the response of modes of whole structure with attached heterogeneities. The method presented here gives a prediction of plate vibration using a wave decomposition instead of modal calculation. It allows one to consider homogeneous structure of complex geometry without making mode calculations before. The corresponding wave function of the Fourier transform of the displacement is approximated the best by achieving the extremalization of the Hamiltonian of the plate. Quadratic velocity of the structure is derived and the convergence study of the method shows that global quantities involving frequency average can be obtained with reduced models of small size.