A modal hybridization method for vibroacoustic studies at medium frequencies

Abstract

A general size reduction procedure of large modal models is set up by means of Ritz–Galerkin projection techniques based on a reduced set of hybrid modes defined in each frequency band by an appropriate linear combination of the eigenmode shapes of the modal reference model. This method applies in the case of ‘‘broadband excitation’’ such as transient or random forces and leads in this case to good estimates of the vibration energy and of response maxima. It appears that the present approach differs from the well-known SEA mainly by accounting for the specificity of the external (or coupling) loads−an appropriate space averaging of the MHM leading to equipartition of energy and therefore to the SEA results. In a first part, this method is introduced in the modal analysis of the response of a structure to external forces (resp. to a prescribed motion) imposed on its interaction surface. It is shown that the hybrid modes cumulate the modal excitabilities (resp. the effective modal masses) of the ‘‘component modes.’’ The second part is devoted to the coupled vibroacoustic problem viewed through the coupling of two sets of acoustic and structure oscillators. It is shown that the resonant coupling problem can be reduced−in each frequency band−to the coupling of N acoustic hybrid modes with N structure hybrid modes corresponding to the N predominant singular values of the (rectangular) coupling matrices (additional structure hybrid modes must be considered for accounting for the external loading). The explicit solution of this problem is given in the case of a frequency band in which a cluster of modes of one subsystem is coupled with a single mode or a pair of modes of the other subsystem.