Static correction of acoustic models with application to vibro-acoustic coupling

Jean-Marie Lagache , Samir Assaf

A direct determination of modal remainders in truncated modal series, in structural or acoustic analyses, has been recently proposed by the authors, leading to explicit expressions of the response of a free-floating mechanical system or of an acoustic cavity, by “accelerated” modal formulae including static terms and accelerated modal series. The general method,- termed “Method of Orthocomplement”,- will be recalled in the paper, especially the pseudo-inversion techniques required by the singular static terms. Since the coupling of an acoustic cavity results from the reduction of the acoustic dynamic stiffness, inv(H – Qw²), to generalized degrees of freedom defined by the coupling matrix, it will be shown that applying the preceding formulae leads to two possible vibro-acoustic methods: (1) a low frequency method based on the algebraic computation of static terms, which delivers the added stiffness and mass matrices to be used from the Helmholtz 0Hz frequency to the first non-zero acoustic frequency; (2) a general method where the static terms are complemented by a reasonable number of cavity modes.

Mots clés: modal series; static correction; model reduction; vibroacoustic

Domaines: Acoustique [physics.class-ph]

Jean-Marie Lagache, Samir Assaf. Static correction of acoustic models with application to vibro-acoustic coupling. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00811214⟩