Prediction of vibrations using a wave sampling decomposition

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 systems. In the idea of reducing these models, a mode hybridization method [H. J-P. Morand, ‘‘A modal hybridization method for the reduction of dynamic models in the medium frequency range,’’ Proceedings of the European Conference on New Advances in Computational Structural Mechanics (1991)] gives one equivalent mode obtained with modes of the complex structure. Another method [D. Trentin and J. L. Guyader, ‘‘Vibrations of a master plate with attached masses using modal sampling method,’’ J. Acoust. Soc. Am. (to be published)] 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. 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. [Work supported by the Institut National de Recherche et de Sécurité and by the Centre National d’Etudes Spatiales.]