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sides. The air and fiber inside the sound -absorbing materials of the monolithic
muffler will vibrate when sound waves enter into the monolithic muffler. Because of
the friction and viscous resistance, the part of the sound energy transform into heat
and dissipate. As the sound wave transmit in the channel, the sound can continue to be
absorbed by sound-absorbing materials. And its sound pressure decreases as the
increasing of the transmission distance. Thus reduce the noise [4]. The length of
muffler is 1.25m, and there is the glass-silk sound- absorbing material inside the
muffler, and the entire muffler is divided into the four same channels by the three
sound-absorbing material boards.
2 The Acoustic Field Simulation of the Monolithic Muffler
2.1 The Control Equations of the Monolithic Muffler
As a macroscopic physical phenomenon, the vibration of sound waves should satisfy
the basic laws of physics, such as Newton's second law, law of conservation of mass
and the state equation of description of temperature, pressure and density. We can
descript the changing relations of sound pressure, particle velocity and density in the
quantitative mathematical form and thus obtain and establish the changing relations of
sound pressure over time and space, namely wave equation. when analysis the
theories of acoustic wave movement, we makes the following basic assumptions
about its transmission process [5][6]: (1) the medium is the uniform ideal fluid, which
is no viscosity, (2) the acoustic transmission process is a adiabatic processes, that is,
no heat exchange with the outside (3) what we descript is the small amplitude
acoustic wave propagation, the change of state of the medium is linear.
The equations of motion
v
uv
∂
v
∇=−
p
ρ
0
∂
t
(1)
v vvv
uv
v
v
v
∂∂ ∂
vvivjvk
=+ +
∇=
+ +
∂∂ ∂
i
j
k
x
y
z
x
y
z
uv
Where:
∇
--the Laplacian,
P-- pressure of the particle, kPa;v -- velocity of the particle, m/s; ρ
0
-- density of the
medium, kg/m
3
;
The equation of continuity
uv v
ρ
∂
ρ
'
−∇=
∂
.
v
0
(2)
The equation of state
Because the sound waves transmit much faster than the speed of heat, we can assume
that the process of sound transmission is adiabatic process. Thus equation of the
adiabatic state of a certain quality of an ideal gas is as follow:
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