A. Debray Contribution to the study of dissipative silencers : effect of structural vibrations, effect of flow 2000

(1)

(2)

(3)

(4)

(5)

x hard wall

d y

(6)

frequency (Hz) frequency (Hz)

0 2000 4000 6000 8000 10000

ï150 ï100 ï50 0

0 2000 4000 6000 8000 10000

0 50 100 150 200

(7)

R z

r

hard wall

(8)

frequency (Hz) frequency (Hz)

0 2000 4000 6000 8000 10000

ï200 ï150 ï100 ï50 0

0 2000 4000 6000 8000 10000

0 50 100 150 200

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

porous material

L

0 z

perforated

screen

(25)

(26)

(27)

0 0.2 0.4 0.6 0.8 1 0

0.2 0.4 0.6 0.8 1

a Rh(a)

(28)

frequency (Hz) frequency (Hz)

0 500 1000 1500

ï25 ï20 ï15 ï10 ï5 0

0 500 1000 1500

0 10 20 30 40 50

frequency (Hz) frequency (Hz)

0 500 1000 1500

ï75 ï70 ï65 ï60 ï55 ï50 ï45 ï40 ï35

0 500 1000 1500

0 10 20 30 40 50

radial position (m) radial position (m)

0 0.01 0.02 0.03 0.04 0.05

ï0.5 ï0.4 ï0.3 ï0.2 ï0.1 0 0.1 0.2

0 0.01 0.02 0.03 0.04 0.05

0.9 0.92 0.94 0.96 0.98 1

(29)

radial position (m) radial position (m)

0 0.01 0.02 0.03 0.04 0.05

ï0.5 0 0.5 1 1.5 2

0 0.01 0.02 0.03 0.04 0.05

0 2 4 6 8 10 12 14 16 18

(30)

(31)

z

0

(32)

(33)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

(34)

(35)

(36)

(37)

(38)

wall rigid impervious porous material

Front view Side view

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(40)

(41)

(42)

(43)

.

(44)

(45)

(46)

(47)

(48)

(49)

(50)

(51)

hard wall

(52)

(53)

(54)

(55)

. . .

.

(56)

(57)

(58)

(59)

(60)

frequency (Hz) frequency (Hz)

0 200 400 600 800 1000

ï10 ï8 ï6 ï4 ï2 0

0 200 400 600 800 1000

0 20 40 60 80 100 120 140

(61)

5 10 15 20 25 30 35 40 45 ï16

ï14 ï12 ï10 ï8 ï6 ï4 ï2 0

0 20 40 60 80

ï9 ï8 ï7 ï6 ï5 ï4 ï3 ï2 ï1 0

(62)

frequency (Hz) frequency (Hz)

0 200 400 600 800 1000

ï10 ï8 ï6 ï4 ï2 0

0 200 400 600 800 1000

0 20 40 60 80 100 120 140

(63)

5 10 15 20 25 30 35 40 ï25

ï20 ï15 ï10 ï5 0

0 10 20 30 40 50 60

ï10 ï8 ï6 ï4 ï2 0

(64)

0 0.5 1 1.5 2 2.5 3 ï200

ï150 ï100 ï50 0 50 100 150 200

mode 1 mode 2

mode 3

(65)

ï20 ï1.5 ï1 ï0.5 0 0.5 1 1.5 2 0.5

1 1.5 2 2.5 3

x=1

x=0

30.4 30.6 30.8 31 31.2 31.4 31.6 31.8 32

ï1.2 ï1 ï0.8 ï0.6 ï0.4 ï0.2 0 0.2 0.4

x=1

x=0

(66)

51.6 51.8 52 52.2 52.4 52.6 52.8 53 53.2 53.4 ï0.4

ï0.2 0 0.2 0.4 0.6 0.8 1 1.2

1.4

x=0

x=1

x x

0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0 0.2 0.4 0.6 0.8 1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

(67)

x x

0 0.2 0.4 0.6 0.8 1

ï0.5 ï0.4 ï0.3 ï0.2 ï0.1 0

0 0.2 0.4 0.6 0.8 1

31.25 31.3 31.35 31.4 31.45

x x

0 0.2 0.4 0.6 0.8 1

ï0.8 ï0.7 ï0.6 ï0.5 ï0.4 ï0.3 ï0.2 ï0.1 0

0 0.2 0.4 0.6 0.8 1

52.35 52.36 52.37 52.38 52.39 52.4

(68)

(69)

(70)

(71)

(72)

(73)

(74)

(75)

(76)

(77)

(78)

(79)

(80)

(81)

imaginary part of impedance

real part of impedance

frequency (Hz) frequency (Hz)

0 1000 2000 3000 4000 5000

ï30 ï25 ï20 ï15 ï10 ï5 0 5

0 1000 2000 3000 4000 5000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

imaginary part of impedance

real part of impedance

frequency (Hz) frequency (Hz)

0 1000 2000 3000 4000 5000

ï35 ï30 ï25 ï20 ï15 ï10 ï5 0 5

0 1000 2000 3000 4000 5000

0 0.5 1 1.5 2 2.5 3 3.5

(82)

imaginary part of impedance

real part of impedance

frequency (Hz) frequency (Hz)

0 1000 2000 3000 4000 5000

ï30 ï25 ï20 ï15 ï10 ï5 0 5

0 1000 2000 3000 4000 5000

0 0.5 1 1.5 2 2.5

(83)

(84)

termination

muffler

acoustic source

acoustic source downstream 4 microphones upstream

fan

thermometer thermometer

PC

HP 3566/67 A flowmeter

anechoic 4 microphones

lined expansion

chamber

(85)

(86)

frequency (Hz) frequency (Hz)

modulus of T

modulus of R

0 500 1000 1500

10^ï5 10^ï4 10^ï3 10^ï2 10^ï1 10⁰

0 500 1000 1500

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

frequency (Hz) frequency (Hz)

modulus of T

modulus of R

0 500 1000 1500

10^ï3 10^ï2 10^ï1 10⁰

0 500 1000 1500

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

frequency (Hz) frequency (Hz)

modulus of T

modulus of R

0 500 1000 1500

10^ï4 10^ï3 10^ï2 10^ï1 10⁰

0 500 1000 1500

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

(87)

frequency (Hz) frequency (Hz)

modulus of T

modulus of R

0 500 1000 1500

0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 500 1000 1500

10^ï8 10^ï6 10^ï4 10^ï2 10⁰

modulus of R modulus of T

frequency (Hz) frequency (Hz)

0 500 1000 1500

10^ï3 10^ï2 10^ï1 10⁰

0 500 1000 1500

0.65 0.7 0.75 0.8 0.85 0.9

(88)

modulus of R modulus of T

frequency (Hz) frequency (Hz)

0 500 1000 1500

10^ï3 10^ï2 10^ï1 10⁰

0 500 1000 1500

0.65 0.7 0.75 0.8 0.85 0.9

modulus of R modulus of T

frequency (Hz) frequency (Hz)

0 500 1000 1500

10^ï4 10^ï3 10^ï2 10^ï1 10⁰

0 500 1000 1500

0.65 0.7 0.75 0.8 0.85 0.9

modulus of R modulus of T

frequency (Hz) frequency (Hz)

0 500 1000 1500

10^ï4 10^ï3 10^ï2 10^ï1 10⁰

0 500 1000 1500

0.65 0.7 0.75 0.8 0.85 0.9

(89)

D C B

A

(90)

(91)

frequency (Hz) frequency (Hz)

0 500 1000 1500

ï60 ï50 ï40 ï30 ï20 ï10 0

0 500 1000 1500

0 50 100 150 200

frequency (Hz) frequency (Hz)

0 500 1000 1500

ï12 ï10 ï8 ï6 ï4 ï2 0

0 500 1000 1500

0 5 10 15 20 25 30 35 40 45

(92)

frequency (Hz) frequency (Hz)

0 500 1000 1500

ï12 ï10 ï8 ï6 ï4 ï2 0

0 500 1000 1500

0 5 10 15 20 25 30 35 40

frequency (Hz) frequency (Hz)

0 500 1000 1500

ï50 0 50 100 150 200

0 500 1000 1500

ï60 ï50 ï40 ï30 ï20 ï10 0

(93)

(94)

(95)

(96)

Multi-layered or porous material

Impervious rigid wall

Plane wave

(97)

10 cm 3 cm material 1 3 cm

material 1

(98)

0 200 400 600 800 1000 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

m=100000

frequency (Hz)

Absorption

m=300000

m=10000

m=1000

100² 10³ 10⁴

10 20 30 40 50 60

frequency (Hz)

Attenuation (dB/m)

(99)

lining

10² 10³ 10⁴

0 10 20 30 40 50 60

frequency (Hz)

Attenuation (dB/m)

(100)

100² 10³ 10⁴ 10

20 30 40 50 60

frequency (Hz)

Attenuation (dB/m)

100² 10³ 10⁴

0.2 0.4 0.6 0.8 1

frequency (Hz)

Absorption

(101)

3 cm

3 cm 20 cm

material 1

(102)

100² 10³ 10⁴ 10

20 30 40 50 60 70

frequency (Hz)

Attenuation (dB/m)

0 500 1000 1500 2000 2500 3000

0 0.2 0.4 0.6 0.8 1

frequency (Hz)

Absorption

(103)

0 200 400 600 800 1000 10

20 30 40 50 60 70 80

frequency (Hz)

Attenuation (dB/m)

2000 400 600 800 1000

20 40 60 80 100 120

frequency (Hz)

Attenuation (dB/m)

(104)

0 200 400 600 800 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

frequency (Hz)

Absorption

0 200 400 600 800

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

frequency (Hz)

Absorption

(105)

2 cm 20 cm 2.81 cm

2.81 cm material 1

plate material 3

2 cm

0 200 400 600 800

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

frequency (Hz)

Absorption

(106)

0 200 400 600 800 0

1 2 3 4 5 6 7 8 9

frequency (Hz)

Attenuation (dB/m)

(107)

(108)

(109)

(110)

(111)

(112)

(113)

II I

L

III porous material

z=L z=0

a b

z

(114)

(115)

(116)

(117)

ï4000 ï2000 0 2000 4000 ï1500

ï1000 ï500 0 500 1000 1500

ï30 ï20 ï10 0 10 20 30

ï100 ï50 0 50 100

(b) (a)

ï600 ï400 ï200 0 200 400 600 ï800

ï600 ï400 ï200 0 200 400 600 800

ï5 0 5

ï60 ï40 ï20 0 20 40 60 80

(b)

(a)

(118)

(119)

(120)

(121)

(122)

(123)

(124)

0 500 1000 1500 0.3

0.4 0.5 0.6 0.7 0.8 0.9 1

0 500 1000 1500

10

^ï3

10

^ï2

10

^ï1

10

⁰

(125)

0 500 1000 1500 0.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 500 1000 1500

10

^ï4

10

^ï3

10

^ï2

10

^ï1

10

⁰

(126)

(127)

0 500 1000 1500 0.3

0.4 0.5 0.6 0.7 0.8 0.9 1

0 500 1000 1500

10

^ï3

10

^ï2

10

^ï1

10

⁰

(128)

0 500 1000 1500 0.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 500 1000 1500

10

^ï4

10

^ï3

10

^ï2

10

^ï1

10

⁰

(129)

(130)

(131)

(132)

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(134)

(135)

(136)

(137)