Convergence of the modal sampling method in the medium frequency range

Abstract

At medium frequencies, several problems deal with systems with a large number of modes. This is encountered, for instance, in the aerospace field. In that case, the evaluation of the vibration behavior using classical modal methods must cope with resolution of huge linear systems and specific methods have to be developed. The modal sampling method, which has been presented in the case of a long beam in longitudinal motion [J. L. Guyader, J. Acoust. Soc. Am. 88, 2269–2276 (1990)], enables one to reconstitute the vibration response of a structure using a limited number of groups of modes, called a sample. The accuracy of the prediction can be improved by increasing the size of the sample. The modal sampling method is presented here in the case of a large, thin, rectangular plate where point masses can be added. The structure is excited by an harmonic point force or a plane acoustic wave and kinetic energy on the structure can be derived. A study of the convergence of the method is presented when the size of the sample is increased and results show the ability of the method to take into account structural heterogeneities. [Work supported by the Institut National de Recherche et de Sécurité and by the Centre National d’Etudes Spatiales.]