Design of Partial Enclosures. D. W. Herrin, Ph.D., P.E. University of Kentucky Department of Mechanical Engineering

Transcription

1 D. W. Herrin, Ph.D., P.E. Department of Mechanical Engineering

2 Reference 1. Ver, I. L., and Beranek, L. L. (2005). 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),

3 Overview Introduction Sound transmission through panels Sound transmission through leaks and openings Noise reduction by absorption material 3

4 Partial Enclosure Leaks Baffle Silencer Enclosure Wall Source Structure-borne flanking 4

5 Source Path Receiver Map Engine surface Engine Compartment Enclosure Panels Engine surface Engine Compartment Openings Baffle Outlet Engine Mounts Isolators Base Enclosure Isolation Enclosure Panels Exterior air Engine Exhaust Muffler 5

6 Overview Introduction Sound transmission through panels Sound transmission through leaks and openings Noise reduction by absorption material 6

7 Beranek, 1960 Sound Transmission Through Thin Panel 7

8 Region 1 Below 1 st Panel Resonance The response is determined by the panel s static stiffness. Higher stiffness, higher transmission loss. At and Above 1 st Panel Resonance The response is determined by the resonant modes. 8

9 1 st Panel Resonance For simply-supported rectangular panel: f (n x, n y ) = π 2! Eh 2! ## 12ρ # "" n x L x $ & % 2! + n y # " L y $ & % 2 $ & & % y where: E Young s modulus H plate thickness ρ density N x x mode index N y y mode index L x plate width in x direction plate width in y direction L y L x x L y 9

10 Panel Resonances First 4 modes of a 30 square steel plate which is thick. 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 If possible, avoid first several resonances in the frequency range of interest. Mode shape Frequency Hz Hz 10

11 Region 2 Limp Panel Theory Assumption: Panel is homogeneous Stiffness and damping ignored mass only Incident Ae ikx Panel velocity Reflected ikx Be Ce ikx Transmitted Radiated ikx C'e x=0 11

12 Normal Incidence Transmission Loss Define τ transmission coefficient: Ae ikx τ = I I t i = C A 2 2 ρ c 0 ρ c 0 = C A = 1+ ( ωρ / 2ρ c) s 0 1 ωρ / 2ρ c s 0 ikx Be where: Ce ikx ρs = m / S Panel surface density ikx C' e 1 TL0 = 10Log10 = 20Log10( ρs f ) 42 τ db x=0 Mass Law: Higher surface density, higher TL. 12

13 Ver and Beranek, 2005 Oblique Incident Sound Transmission Diffusive sound field: plane waves of the same average intensity travelling with equal probability in all directions. τ =τ (φ) τ = ϕ lim 0 τ (ϕ)cosϕ sinϕ dϕ ϕ lim 0 cosϕ sinϕ dϕ For random incidence ϕ lim = 90 TL Random = TL 0 10 log10(0.23tl0 ) For field incidence (better agreement with measurement) ϕ lim = 78 TL = Field TL 5 0 db 13

14 Field Incidence Theoretical sound transmission loss of large panels for frequencies in Region 2: 14

15 Ver and Beranek, 2005 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. where: f C = 2 c 2π ρs D ρs = m / S 3 Eh D 12(1 v 2 ) Panel surface density = Bending stiffness of plate 15

16 Radiation Efficiency In thin plates, the dominating vibration will be bending vibration. Unlike an acoustic wave, bending wave speed is dependent on frequency. Plate bending c p Dω 2 2π = 4 λ p = 4 ρs f Sound in air D ρ S Wavelength(m) Sound in the air 0.20 steel plate 0.15 steel plate 0.10 steel plate λ a = c f Frequency(Hz) 16

17 Radiation Efficiency λ p << λ a l=l + -l - 0 λ p λ a l >> 0 The plate will perform like closely distributed out-of-phase sources. l + l - l + l

18 Wallace, 1972 Radiation Efficiency Define radiation efficiency: W σ = 1 ρcs 2 2 V N where: W Actual energy radiated V N Mean square normal velocity S Panel area σ Around and above critical frequency, the thin panels are very efficient radiator. λ p / λ a 18

19 Sharp, 1973 Effect of Thickness Increase TL according to Mass Law TL 20 ( 0 = Log10 ρhf ) 42 h Shift critical frequency above range of interest f C = 2 c 12(1 v 2π Eh 2 3 ) ρ S h Poses a dilemma due to inconsistent requirement. 19

20 Sharp, 1973 Various Designs Laminated Panels Single 1-inch and two 1/2-inch spot laminated sheets of gypsum board 20

21 Wallin, Carlsson, Abom, Boden, and Glav, 2001 Double Panels Fundamental resonant frequency: 3 f 0 = 1 2π 2 ρ0c ʹ d ρ S ρʹ S = ρs1ρs 2 ρ + ρ S1 S 2 1 f 0 2 f l Cavity resonant frequency: f n f 2 d f 1 = c 2d f 1 c f2 = fn = d nc 2d f c = l 2πd = f1 π 21

22 Sharp, 1973 Double Panels Transmission loss of double panels calculated using approximate method: TL = 20Log10( ρ f ) 47 S f < f 0 TL = TL1 + TL log10(2kd) f < f < 0 f l TL = TL TL f > f l 22

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. 23

24 Overview Introduction Sound transmission through panels Sound transmission through leaks and openings Noise reduction by absorption material 24

25 Kang, 2001 Transmission Coefficient The angle-averaged sound transmission coefficient through a small slit: τ = I I t i = mk n sin K( L + 2e) + 2K TL = 10Log10 1 τ where K = kd L = t d e = β d d 8 β = ln π K 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 25

26 Insertion Loss with Leaks The reduction in insertion loss due to leaks: ΔILL 10log 1 γ = S j S W 10 j (1 + γ TL j 10 TL W /10 ) For preliminary calculations: TL j = 0 γ 1 = S S j j W where: γ leak ratio factor TL W transmission loss of the enclosure walls S W total area of enclosure walls S j area of j th leak TL j transmission loss of the j th leak 26

27 Insertion Loss with Leaks IL (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. TL W (db) 27

28 Treatment with Ventilation Openings Untreated Treated 28

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. 29

30 Overview Introduction Sound transmission through panels Sound transmission through leaks and openings Noise reduction by absorption material 30

31 Absorption materials Flow Resistivity σ Sample Thickness t P u (velocity) Vacuum source Absorption coefficient Flow resistivity: σ = ΔP ut Fluid Flow resistivity Solid 31

32 Absorption Materials Closed and Open Cell Absorption coefficient Frequency (Hz) 32

33 Absorption Materials Effect of Thickness Absorption coefficient Frequency (Hz) 33

34 Absorption Materials Adding Mass Cover Absorption coefficient Frequency (Hz) 34

35 Summary 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.) 35

36 Control Engineering edited by Beranek and Ver, 1992 Overview Insertion Loss IL = L WO L WE db Good Performance Measure Can be Negative Enclosure increases sound 36

37 Left Test Case Top 0.48 x 0.48 x 0.66 m 3 Opening of radius m Top and left panels (1 mm thick steel) All other panels (2 mm thick steel) 37

38 Measurement Setup Sound Absorption Material Wood Blocks Opening Area 38

39 Enclosure Modes f lmn = 2 c l 2 m n + + Lx Ly Lz 2 2 l, m, n = 0, 1, 2, 3 N f0,0,1 = 260 Hz f 0,0,2 = 519 Hz 39

40 Indirect BEM Field Point Mesh Impedance Opening (Zero Pressure Jump) Symmetry Plane 40

41 Modeling Approach Source Geometry Source Geometry 41

42 Modeling Approach Source Geometry Insertion Loss (db) Measurement Simulation (No Source Geometry) Simulation (Source Geometry) Frequency (Hz) 42

43 Modeling Approach Panel Absorption Add low absorption to panels 43

44 Modeling Approach Panel Absorption Insertion Loss (db) Measurement Simulation (No Low Absorption) Simulation (Low Absorption) Frequency (Hz) 44

45 Modeling Approach Coupling Vibrating Plate 45

46 Modeling Approach Coupling Insertion Loss (db) Measurement Simulation (No Coupling) Simulation (Coupling) Frequency (Hz) 46

47 Validation Test Two Openings Additional Opening Original Opening 47

48 Validation Test Two Openings Absorbent Material Two Openings Field Point Mesh Ground 48

49 Validation Test Increased Open Area Insertion Loss (db) 0-20 Measurement Simulation Frequency (Hz) 49