Civil Engineering Reference
In-Depth Information
12
Extensions to the transfer
matrix method
12.1
Introduction
This chapter discusses various extensions and applications of the transfer matrix method
(TMM). First, corrections to account for size effects in absorption and transmission loss
problems are presented with validation examples. Next, the application of the method to
point load excited panels with attached sound packages is discussed.
12.2
Finite size correction for the transmission problem
The classical transfer matrix method assumes a structure of infinite extent. For trans-
mission loss application, the method correlates well with experiments at mid to high
frequencies for a large range of flat panels. Discrepancies are however observed at low
frequencies, especially for panels of small size. This section presents a simple geomet-
rical correction to account for this 'geometrical' finite size effect (Ghinet and Atalla,
2002). The rationale behind the approach presented is to replace the radiation efficiency
in the receiving domain by the radiation efficiency of an equivalent baffled window. This
approach is thus strictly valid for planar structures.
12.2.1 Transmitted power
Consider a baffled panel of area
S
excited by a plane incident wave with heading
angles
(θ,φ)
p
i
(M)
=
exp
−
jk
0
(
cos
φ
sin
θx
+
sin
φ
sin
θy
+
cos
θz)
(12.1)
