Sound transmission. Characterization and properties of single walls and floors - Building Acoustics - page 252

in industrial buildings are plates where the corrugations have a trapezoidal shape,
commonly called cladding. We have previously (see section 3.7.3.3) referred to the
literature giving the equivalent components of stiffness for such plates, enabling us to
apply the general theory for plane orthotropic plates. We also performed a calculation of
natural frequencies for a “wave”-corrugated plate.
The advantage of corrugated plates is great strength as compared to weight. They
are more lightweight and cheaper than plane plates having equal strength. The
disadvantage, however, is that the sound reduction index may become much less than for
plane plates of equal thickness. We shall use the symbol B 1 to denote the bending
stiffness (per unit length) about an axis lying in the plane of the plate normal to the
corrugations, i.e. about the z-axis of Figure 6.26 . Correspondingly, B 2 is the bending
stiffness about the x-axis. We shall then find two critical frequencies given as

2 2

c c

m m

0 0

f = og f = , (6.107)

c1 c2

2 π B 2 π B

1 2

where m as usual represents the mass per unit area. The corrugations may increase the
bending stiffness considerably, which certainly is the purpose, but it is followed by a low
value of f c1 . This implies that the resonant transmission may become the dominant factor
over a large part of the useful frequency range.

Y

ϕ

θ

X

Z

Figure 6.26 Corrugated plate with incident sound wave in direction (ϕ , θ).

Certainly, there are a multitude of such plates in use. With some there is a relatively
small difference between the stiffness components, which makes the difference small
between the critical frequencies. The coincidence range with the typical dip in the sound
reduction curve will then just be a little broader. Commonly, however, the difference in
stiffness is much larger. Whereas f c1 could be in the range of some hundred hertz, the
corresponding f c2 could be 15-30 kHz.
Instead of Equation (6.91) we get an expression for the wall impedance Z w
dependent on two critical frequencies, at the same time dependent on two angles. In
addition to the angle of incidence φ, the angle to the plate normal, the impedance will be
a function of the azimuth angle θ as well. We get (see e.g. Hansen (1993)