Civil Engineering Reference
In-Depth Information
This solution procedure is straightforward and necessitates only the solution of a
linear system at each frequency and/or incidence angle.
11.6.3 Piston excitation
From a transfer matrix viewpoint, a piston is equivalent to a plate with a fixed normal
velocity. The variable vector is given by
V
p
(A)
[
p(A),v
3
(A)
]
T
where the velocity
is fixed. The continuity conditions between the excitation (the piston) and the first layer
are discussed in Section 11.4. Using these interface conditions, the solution approach
remains unchanged. The example of a semi-infinite fluid termination is presented here
for the sake of illustration. Since the piston's velocity is given, the second column of
matrix [
D
], given in Equation (11.85), is eliminated, resulting in a square matrix denoted
by [
D
2
]. Let
F
represent the vector obtained by multiplying the eliminated second column
by
−
1. Finally, let
V
2
represent the variable vector less its second entry. The solution
procedure is as follows.
First, the (
N
=
+
1
)
×
(N
+
1) linear system [
D
2
]
V
2
=
F
is solved for vector
V
2
.Next,
the acoustic variables are calculated:
p(A)
=
V
2
(
1
)
p(B)
=
V
2
(N
−
1
)
v(B)
(11.99)
=
V
2
(N)
Using these variables, various vibro-acoustic indicators can be calculated. For
example, the mechanical to acoustical conversion factor, defined as the ratio of the
power radiated in the receiver domain to the input power is given by
TL
=−
10 log
10
radiated,free face
input
(11.100)
with
radiated,free face
=
1
/
2Re
(p(
B
)υ
∗
(
B
))
and
input
=
1
/
2Re
(p(A)υ
∗
(A))
.
The fraction of dissipated power, defined by the difference between input mechanical
power and power transmitted to the receiver domain, is given by
DP
=−
10 log
10
dissipated
input
(11.101)
with
dissipated
=
input
−
radiated
.
Finally, the vibration transmissibility, defined by the ratio of the free face vibration
level to the imposed velocity, is given by
VT
=−
10 log
10
v
2
piston
(11.102)
v
2
free - face
Note that the use of the transfer matrix method in the case of a point load excitation
is discussed in Chapter 12. The case of a point source excitation is also briefly discussed
in Chapter 12.
