Page 708 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Interior noise: Assessment and control C HAPTER 21.1

2
over the edges of the panel. Any acoustic leaks become where E is the Young’s modulus (N m ) and l is the
4
4
immediately apparent. The fitting of quality acoustic moment of inertia (m or beware, commonly mm ).
seals is one of the reasons for the relatively high cost of For plates of thickness h the moment of inertia per
0
acoustic encapsulation. One of the major challenges in unit width l is used
enclosure design is the provision of adequate ventilation
and cooling without causing leakage of sound. 0 h 3
I ¼ (21.1.123)
Flanking transmission must be controlled if an enclo- 12
sure is to be fully effective. A common flanking path is
due to vibration from the noise source being transmitted and the bending stiffness becomes:
into the floor of the enclosure and either producing re- I E
0
0
radiated sound outside the enclosure or forcing the walls B ¼ 2 (21.1.124)
of the enclosure into vibration and this seriously limits 1 m
their TL characteristics. An obvious example is the in- The velocity at which one must travel to remain
terior noise due to an IC engine where structure-borne always at the same phase of one infinite sinusoidal wave is
noise is in effect a flanking path. the phase velocity of bending waves
Care should be taken that pipes and service ducts
crossing the boundary of the enclosure are well isolated r ffiffiffiffiffi ffiffiffiffi
B p
from the structure of the enclosure. Particular care c B ¼ 4 0 2 uðms 1 Þ (21.1.125)
should be taken if forced ventilation is being provided as m
in the case of an enclosure around an IC engine. where m is the mass per unit length (rS ) and u is the
0
1
radial frequency (rad s ):
21.1.10.5 The transmission of sound u ¼ 2pf f is the frequency ðHzÞ (21.1.126)
through panels
For plates of thickness h, this becomes (providing that
Vibration may propagate through a structure in the form the wavelength l [ 6h)
of compressional, shear or torsional waves. In structures
constructed with thick members all three types of prop- q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffiffiffiffiffiffiffiffiffi
1:8h
agation may be significant. However, in thin panels pure c B z 1:8c L I hf ¼ c L I ðms 1 Þ (21.1.127)
compressional propagation is not likely, and in the audio l L I
frequency range such panels are usually excited by sound s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
to form bending waves which are a combination of com- ¼ E (21.1.128)
c L i 2
pression and shear motions. Bending waves result in r ð1 m Þ
m
a deflection of the panel in a direction that is normal to its
surface. The spatial distribution of this deformation is where r m is the material density and m is Poisson’s
a function of the bending wave speed. ratio.
1
The speed of propagation of sound in air c (m s )is Note that the phase velocity is frequency-dependent
a function of the composition of the fluid and of and therefore the wavefront distorts (dispersion) as
temperature higher-frequency components propagate with higher
phase velocity than lower-frequency components.
p ffiffiffiffiffiffiffiffiffiffi
c ¼ gRT (21.1.121) One may demonstrate that energy propagates at the
group velocity C B (see p. 106 of Cremer and Heckl
where (1988) for details)
g ¼ c p /c v ratio of specific heats 1
R ¼ gas constant C B ¼ 2c B ðms Þ (21.1.129)
T ¼ temperature (K) It should be noted that practical panels are unlikely to
Interestingly, the speed of propagation of bending be isotropic in construction and therefore bending wave
waves is dependent not only on the mechanical char- speed could vary with direction making the panel
acteristics of the material (Poison’s Ratio, Young’s orthotropic to some extent. However, the isotropic as-
Modulus), but also on the shape and particularly the sumption is convenient and therefore will be pursued
thickness of the panel. Thus for large elements, the further here, particularly as the assumption tends to hold
bending stiffness B is: true as frequency increases and the flexural wavelength
tends towards the characteristic dimension (usually
B ¼ EI (21.1.122) thickness) of the panel.

719