Building Acoustics

232 Building acoustics

considerably less differences between stiffened and non-stiffened panel. (How would
you explain this?)
Furthermore, it should be mentioned that a clamped plate would normally radiate
sound better than a simply supported one. On the other hand, a freely suspended plate
could create an acoustical “short-circuiting” between back and front, i.e. behaving like a
dipole and thereby reducing the radiation. A pronounced example on such acoustical
short-circuiting is to be found in perforated plates, which may exhibit very small
radiation factors. In noise control of machinery this effect is well known and perforated
panel are used in enclosures for e.g. rotating parts. This will reduce the radiated noise
from the enclosure if being mechanically excited by the machine. Certainly, it will not
act like an acoustical enclosure or barrier, if this should be the purpose of the shielding.

6.4 Bending wave generation. Impact sound transmission

In section 6.3, the subject was sound radiation from a plate assuming that, in one way or
another, it had been set into vibrations and thus obtained a velocity or velocity
distribution. The pertinent question to be asked is therefore: How shall we find the
velocity or velocity distribution induced by a given excitation of a structure having a
certain shape, dimensions and material properties? Again, we shall only be concerned
with plate structures and the types of excitation will either be a sound pressure
distribution over the surface or mechanical point forces. We shall start with the latter
being relevant for the problem of impact sound.

6.4.1 Power input by point forces. Velocity amplitude of plate

In Chapter 3 (section 3.7.3.4), we presented an example of the response of a plate excited
by a point force. We calculated the input mobility M in a given point defined by

0

1m

.

Ns

u

M

FZ

⎛⎞

== ⎜⎟

⎝⎠⋅

(6.50)

The quantities u 0 and F represent the velocity and force at this point, respectively, and Z
the corresponding point impedance or input impedance. Corresponding quantities are
defined for moment and angular velocity but we shall limit our treatment to point forces.
For an infinitely large plate, excited into bending vibrations, Cremer et al. (1988)
have shown that the input mobility is a real quantity given by

(^2)

11

,

82.3

M

mB Eρ h

∞=≈

⋅⋅⋅

(6.51)

where the last term is an approximation applicable for homogeneous plates. The
important point to be made concerning Equation (6.51) is that it also represents the mean
value of the mobility of a finite plate, i.e. the mean value taken over all input points and
over frequency. This fact has already been referred to in Chapter 3, where we showed in
Figure 3.23 that the natural modes resulted in a mobility and impedance strongly space
and frequency dependent. The expected or mean value, however, is equal to the one
found for an infinite plate.