### ASA 124th Meeting New Orleans 1992 October

## 3aSA5. A modal hybridization method for vibroacoustic studies at medium
frequencies.

**H. J-P. Mor
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*Ctr. Natl. d'Etudes Spatiales, Direction des Lanceurs, 91023 Evry Cedex,
France
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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.