06 Partial Enclosuresweb.engr.uky.edu/~dherrin/Bandung/08_Partial_Enclosures.pdf · Noise and...

D. W. Herrin, Ph.D., P.E. University of Kentucky

Department of Mechanical Engineering

Design of Partial Enclosures


Noise and Vibration Short Course

Dept. of Mechanical Engineering University of Kentucky

2

Reference

1.  Ver, I. L., and Beranek, L. L. (2005). Noise and Vibration Control Engineering: Principles and Applications. John Wiley and Sons.

2.  Sharp, B. H. (1973). A study of techniques to increase the sound insulation of building elements. U.S. Department of Commerce, National Technical Information Service (NTIS).

3.  Bodén, H., Carlsson, U., Glav, R., Wallin, H., and Åbom, M. (2001). Sound & Vibration. The Marcus Wallenberg Laboratory, KTH.

4.  Kang, H. J., Kim, J. S., Kim, H. S., & Kim, S. R. (2001). Influence of Sound Leaks on In Situ Sound Insulation Performance. Noise Control Engineering Journal, 49(3), 113-119.




3

Overview

  Introduction   Sound transmission through panels   Sound transmission through leaks and openings   Noise reduction by absorption material




4

Partial Enclosure

Source

Enclosure Wall

Leaks

Structure-borne flanking

Baffle Silencer




5

Source Path Receiver Map

Engine surface

Engine Mounts

Engine Exhaust

Openings

Muffler

Exterior air

Engine Compartment

Isolators Base Enclosure

Panels

Baffle Outlet

Enclosure Isolation

Engine surface

Engine Compartment

Enclosure Panels




6

Overview





7

Sound Transmission Through Thin Panel

Beranek, 1960




8

Region 1

Below 1st Panel Resonance   The response is determined by the

panel’s static stiffness.   Higher stiffness, higher transmission

loss.

At and Above 1st Panel Resonance   The response is determined by the

resonant modes.




9

1st Panel Resonance

For simply-supported rectangular panel:

f (nx,ny ) =π2

Eh2

12ρnxLx

!

"#

$

%&

2

+nyLy

!

"##

$

%&&

2!

"

##

$

%

&&

where: E Young’s modulus H plate thickness ρ density Nx x mode index Ny y mode index Lx plate width in x direction Ly plate width in y direction

x

y

Ly

Lx




10

Index Nx=1, Ny=1 Nx=2, Ny=1

Mode shape

Frequency 25.5 Hz 63.7 Hz

Index Nx=2, Ny=2 Nx=1, Ny=3

Mode shape

Frequency 101.9 Hz 127.4 Hz

First 4 modes of a 30’’ square steel plate which is 0.125’’ thick.

If possible, avoid first several resonances in the frequency range of interest.

Panel Resonances




ikxAe−

ikxBe

ikxeC '

ikxCe−

11

Region 2 Limp Panel Theory

Assumption:   Panel is homogeneous   Stiffness and damping ignored – mass only

Incident

Reflected

Radiated

Panel velocity

Transmitted

x=0




12

Normal Incidence Transmission Loss

ikxAe−

ikxBe

ikxeC '

ikxCe−

x=0

Define τ transmission coefficient:

ccAC

cAcC

II

ssi

t

002

2

02

02

2/1

)2/(11

ρωρρωρρ

ρτ ≈

+====

where:

Sms /=ρ Panel surface density

dB42)(20110 10100 −== fLogLogTL Sρτ

Mass Law: Higher surface density, higher TL.




13

Oblique Incident Sound Transmission

  Diffusive sound field: plane waves of the same average intensity travelling with equal probability in all directions.

For random incidence ϕ lim = 90

For field incidence (better agreement with measurement) ϕ lim = 78

)23.0(log10 0100 TLTLTLRandom −=

dBTLTLField 50 −=

τ =τ (ϕ )cosϕ sinϕ dϕ

0

ϕlim∫cosϕ sinϕ dϕ

0

ϕlim∫)(φττ =

Ver and Beranek, 2005




14

Field Incidence

Theoretical sound transmission loss of large panels for frequencies in Region 2:




15

Region 3 Coincidence Effect

This pronounced dip in transmission loss curve occurs when the wavelength of sound in the air coincides with the structural wavelength. This frequency is called critical frequency.

Dcf S

Cρ

π2

2

=

where:

Sms /=ρ Panel surface density

)1(12 2

3

vEhD−

= Bending stiffness of plate

Ver and Beranek, 2005




1000 3000 5000 7000 90000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency(Hz)

Wavelength(m)

16

Radiation Efficiency

In thin plates, the dominating vibration will be bending vibration. Unlike an acoustic wave, bending wave speed is dependent on frequency.

4

2

Sp

Dcρω

= 42

Sp

Df ρπ

λ =

Plate bending

Sound in air

fc

a =λ

Sound in the air 0.20’’ steel plate 0.15’’ steel plate 0.10’’ steel plate




17


- - + + + + + + + +

- - - -

l+ l-

The plate will perform like closely distributed out-of-phase sources.

λp << λa ∆l=l+-l- ≈ 0

- - + + + +

l+

l-

λp ≈ λa ∆l >> 0




18


λp / λa

σ 2

21

NVcS

W

ρσ =

where: W Actual energy radiated VN Mean square normal velocity S Panel area

Define radiation efficiency:

Around and above critical frequency, the thin panels are very efficient radiator.

Wallace, 1972




19

Effect of Thickness

Poses a dilemma due to inconsistent requirement.

42)(20 100 −= hfLogTL ρ

Increase TL according to Mass Law

h

3

22 )1(122 Eh

vcf SC

ρπ

−=

Shift critical frequency above range of interest

h

Sharp, 1973




20

Various Designs

Laminated Panels

Single 1-inch and two 1/2-inch spot laminated sheets of gypsum board

Sharp, 1973




21

Double Panels

0f

1f

2f

nf

lf

dcfSρ

ρπ ʹ′

=2

00 2

1

Fundamental resonant frequency:

21

21

SS

SSS ρρ

ρρρ

+=ʹ′

Cavity resonant frequency:

dcf21 =

dncf

dcf n 22 ==

d

ππ1

2f

dcfl ==

3

21

Wallin, Carlsson, Abom, Boden, and Glav, 2001




22

0ff <

Double Panels

47)(20 10 −= fLogTL Sρ

lfff <<0)2(log20 1021 kdTLTLTL ++=

lff >621 ++= TLTLTL

Transmission loss of double panels calculated using approximate method:

Sharp, 1973




23

Summary

  Panel should be large enough so that the first structural resonance occurs below the frequency range of interest.

  Critical frequency should be shifted above the frequency range of interest (by increasing surface density or lowering bending stiffness of enclosure walls).

  Mass law: below critical frequency, more mass is usually better.   For double panel configuration, avoid cavity resonance in frequency

range of interest.   Damping increases transmission loss at resonant and coincident

frequencies.




24

Overview





25

Transmission Coefficient

The angle-averaged sound transmission coefficient through a small slit:

⎟⎠

⎞⎜⎝

⎛ −=

=

=

=

577.08lnK

ddedtLkdK

πβ

β

222 2)2(sin2 KeLKnmK

II

i

t

++==τ

where

Kang, 2001

τ110 10LogTL =

d width of the slit t depth of the slit

m = 8 for diffuse incidence 4 for normal incidence n = 1 for slit in middle = ½ for slit next to edge




26

Insertion Loss with Leaks

The reduction in insertion loss due to leaks:

∑ −×=

×+≅Δ

j

TLj

W

TLL

j

W

SS

IL10

10/10

101)101(log10

γ

γ

where: γ leak ratio factor TLW transmission loss of the enclosure walls SW total area of enclosure walls Sj area of jth leak TLj transmission loss of the jth leak

For preliminary calculations:

0=jTL ∑= j jW

SS1

γ




27

∆IL

(dB

)

TLW (dB)

For enclosure wall with transmission loss of 40 dB, the leak ratio factor must be less than 10-3 to avoid decrease of insertion loss greater than 10 dB.

Insertion Loss with Leaks




28

Treatment with Ventilation Openings

Untreated Treated




29

Summary

  Reduce the area of leakage if possible.   At air inlet and exhaust, try to seal the leakage.   Avoid direct line of sight between noise source and

receiver.




30

Overview





31

Absorption materials Flow Resistivity σ

∆P

u (velocity)

Vacuum source

Sample Thickness t

Flow resistivity: utPΔ

=σ

Flow resistivity

Abs

orpt

ion

coef

ficie

nt

Fluid Solid




32

Absorption Materials Closed and Open Cell

Frequency (Hz)

Abs

orpt

ion

coef

ficie

nt




33

Absorption Materials Effect of Thickness

Frequency (Hz)

Abs

orpt

ion

coef

ficie

nt




34

Absorption Materials Adding Mass

Cover

Frequency (Hz)

Abs

orpt

ion

coef

ficie

nt




35

  Thicker is generally better to extend absorption to lower frequency

  Working environment needs to be considered when choosing materials (high temperature, water and oil deterioration, etc.)

Summary




36

Overview Insertion Loss

dBWEWO LLIL −=

Noise and Vibration Control Engineering edited by Beranek and Ver, 1992

  Good Performance Measure   Can be Negative

–  Enclosure increases sound




37

  0.48 x 0.48 x 0.66 m3   Opening of radius 0.051 m   Top and left panels (1 mm thick steel)   All other panels (2 mm thick steel)

Top Left

Test Case




38

Measurement Setup

Opening Area

Sound Absorption Material

Wood Blocks




39

222

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

zyxlmn L

nLm

Llcf

Hz2601,0,0 =f Hz5192,0,0 =f

l, m, n = 0, 1, 2, 3 …N

Enclosure Modes




40

Impedance Opening

(Zero Pressure Jump)

Field Point Mesh

Symmetry Plane

Indirect BEM




41

Modeling Approach Source Geometry

Source Geometry




42

Modeling Approach Source Geometry

-45

-30

-15

0

15

30

45

0 200 400 600 800 1000

Frequency (Hz)

Inse

rtion

Los

s (d

B)

Measurement

Simulation (No Source Geometry)

Simulation (Source Geometry)




43

Add low absorption to panels

Modeling Approach Panel Absorption




44

Modeling Approach Panel Absorption

-45

-30

-15

0

15

30

45

0 200 400 600 800 1000

Frequency (Hz)

Inse

rtion

Los

s (d

B)

Measurement

Simulation (No Low Absorption)Simulation (Low Absorption)




45

Modeling Approach Coupling

Vibrating Plate




46

Modeling Approach Coupling

-30

-15

0

15

30

45

0 200 400 600 800 1000

Frequency (Hz)

Inse

rtion

Los

s (d

B)

MeasurementSimulation (No Coupling)Simulation (Coupling)




47

Original Opening Additional Opening

Validation Test Two Openings




48

Two Openings Field Point Mesh

Ground

Absorbent Material

Validation Test Two Openings




49

Validation Test Increased Open Area

-40

-20

0

20

40

0 200 400 600 800 1000

Frequency (Hz)

Inse

rtion

Los

s (d

B)

MeasurementSimulation

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06 Partial Enclosuresweb.engr.uky.edu/~dherrin/Bandung/08_Partial_Enclosures.pdf · Noise and...

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