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Smart Technologies in Vibroacoustics 289
elastic one. The coupling integral combines the boundary integral terms resulting from both
poroelastic and elastic weak forms (Equations (25) and (26), respectively):
CI p-e = σ
Ɣp-e t
ij n
j δui + φ (Ui − ui) ni δp + σ
Ɣp-e Ɣp-e e
ij nej δue i
where n e i =−ni are the components of the unit normal vector pointing outside the elastic
domain (and into the poroelastic medium). Now, the following coupling conditions must be
met at the interface:
(62)
σ t
ij n j = σ e
ij n j , (Ui − ui) ni = 0 , ui = u e i (63)
The first condition states the continuity of the total stress tensor, the second one expresses that
there is no mass flux across the interface and the last one assumes the continuity of the solid
displacements. The last condition also involves the equality of the variations of displacements,
δui = δue i . Now, applying the coupling conditions for the coupling integral (62) results in
CI p-e = 0 (64)
This is similar to the result obtained for coupling between two poroelastic domains: the coupling
between poroelastic and elastic media is also naturally handled [26, 27].
8.6.3 Poroelastic–Acoustic Coupling
Now, the coupling between poroelastic and acoustic media will be discussed. Let Ɣ p-e be an
interface between a poroelastic material and an acoustic medium, with ni being the components
of the unit vector normal to the interface and pointing outside the poroelastic domain (and
into the acoustic medium), whereas na i are the components of the similar unit normal vector
pointing in the opposite direction; therefore, in every point of the interface na i =−ni. The
coupling integral is a combination of the boundary integral terms from the poroelastic weak
form (25) and the acoustic weak form (49):
CI p-a = σ
Ɣp-a t
ij n
j δui + φ (Ui − ui) ni δp +
Ɣp-a 1
Ɣ ω p-a
2 p
ϱa
a |i na i δpa
The coupling conditions between the two media express the continuity of (total) stresses, (total)
normal displacements and pressure, respectively:
σ t
ij n j =−pni ,
1
ω 2 ϱa
p a |i na i = ut i na i
, p = pa
(65)
(66)