Civil Engineering Reference
In-Depth Information
13
Finite element modelling
of poroelastic materials
13.1
Introduction
The vibroacoustic performance of finite multilayer systems containing poroelastic mate-
rials is of the utmost importance for noise control in automobiles, aircraft and several
other engineering applications. In the absence of absorbing materials, the vibroacoustic
response of complex multilayer structures are classically modelled using the finite ele-
ment and the boundary element methods. To account for absorbing media, finite element
formulations for sound absorbing materials have been developed. They range from simple
approaches using equivalent fluid models (Craggs 1978, Beranek and Ver 1992, Panneton
et al
. 1995) to sophisticated approaches based on the Biot theory (Kang and Bolton 1995,
Johansen
et al
. 1995, Coyette and Wynendaele 1995, Panneton and Atalla 1996, 1997,
Atalla
et al
. 1998, 2001a). The latter approaches are mainly based either on the classical
displacement
(
u
s
,
u
f
)
formulation of Biot's poroelasticity equations (Chapter 6) or
the mixed displacement - pressure
(
u
s
,p)
formulation (Appendix 6.A). However, it has
been shown that, while accurate, these formulations have the disadvantage of requiring
cumbersome calculations for large finite element models and spectral analyses. To
alleviate these difficulties, alternative numerical implementations have been investigated.
This chapter reviews various finite element formulations for the modelling of poroelastic
materials with an emphasis on the mixed pressure - displacement formulation. The
presentation is not comprehensive, but aims at giving the reader a general view of the
subject. The generic problem of interest deals with the prediction of the vibroacoustic
response (dynamic and acoustic response) of multilayered structures made up of elastic,
poroelastic and acoustic media. The poroelastic material may be bonded or unbonded
to the structure. The classical assumptions
concerning linear acoustic, elastic, and
