Acoustic Porous Materials and Their Characterisation

Transcription

1 Acoustic Porous Materials and Their Characterisation Kirill V. Horoshenkov School of Engineering, Design and Technology University of Bradford Bradford 1

2 Yorkshire dales Where is Bradford on the map? Bradford city 2

3 Acoustic Research at Bradford University Acoustic materials (Prof. Horoshenkov, Dr. Swift (Armacell UK)) General sound propagation (Prof. Horoshenkov, Prof. Hothersall*, Dr. Hussain) Environmental noise (Prof. Watts (TRL), Prof. Hothersall*, Prof. Horoshenkov) Vibration (Prof. Wood, Prof. Horoshenkov) supported by ~15 PhD/MPhil students (*) visiting professor 3

4 Experimental Facilities at Bradford University Sound propagation experiments Extensive experimental setup for characterisation of material pore structure Extensive experimental setup for measuring acoustic, vibration and structural performance of poro-elastic materials Facilities for poro-elastic material manufacturing 4

5 Topics of Research on Acoustic Materials Development of improved prediction models Experimental investigation of porous media Development of novel, environmental sustainable materials with improved acoustic efficiency 5

6 Where these materials are actually used? 6

7 Automotive insulation Aircraft insulation Noise from electronic cabinets Pipeline insulation 7

8 How these materials look like? 8

9 Consolidated recycled foam Granular mix Virgin reticulated foam Re-constituted foam grains 9

10 What they actually do to sound? 10

11 Effect on room response Propagation in empty enclosure with rigid walls Propagation in enclosure with porous layer speaker mic 11

12 Effect on pipe response (20m long, 600mm concrete pipe) 12

13 How these materials are characterised? 13

14 Impedance tube method BS Sound source Stationary random noise microphone 1 p 1 microphone 2 p 2 Rigid backing l p i mic 3 p r tested sample H ( ω) = p p 2 1 e = ik + e 1+ R ik R R H ( ω) e e ik ( ω) = ik e H ( ) ω 2ikl 14

15 Measuring frequency-dependent dynamic stiffness top accelerometer loading plate (m) tested sample (Z, k) impedance head Z k Mω sin = T cos kl E kl mt + M = l cos ( m+ M ) T shaker = Z ω k 15

16 Armafoam sound 1.00E+06 Real 1.00E frequency, Hz 16

17 Loss factor Frequency (Hz) 17

18 Measuring dynamic stiffness to BS29052 s = ω m Pa m 2 0 [ / ] top accelerometer with dynamic mass shaker bottom accelerometer loading plate tested sample 18

19 Dynamic Stiffness - BS lower stiffnes -30 Relative acceleration level, [db] f 0 Material 1-50 Material 2 Material frequency (Hz) 19

20 Airborne transmission loss (0.5m x 0.5m plate) tested plate 20

21 Averaged Transmission Loss for 0.48m x 0.48m x 47 mm samples of rockwool 5 Transmission Loss, db With skins on Without skins Frequency, Hz 21

22 Airborne transmission loss (99mm sample) 22

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24 Impact sound insulation 24

25 Octave -band level Relative acceleration level, db. Re. 1V Developed sample Cumulus Without material on w ooden base frequency, Hz 25

26 Acoustic Material Modelling of Porous Media 26

27 What is required from an acoustic material model apart from being accurate? 27

28 What else is required from an acoustic material model apart from being accurate? 28

29 Response to a δ-pulse at t = 0 Comparison of some common impedance models. Semi-infinite layer Pade approximation Keith Wilson (A-C-like) analytic models Response to a δ-pulse Miki model Delany and Bazley model R = 250 kpa s m -2 non-analytic models Time, µsec 29

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32 Viscosity correction function In the case of a porous medium with a KNOWN pore size distribution e(s) we can use the Biot s VCF to predict the characteristic acoustic impedance and complex wavenumber: F( ω) 0 0 τ ( ω) e( s) ds, U ( ω) e( s) ds total shear stress on pore walls (1) average seepage velocity Commonly, the function e(s) is substituted with its log-normal fit, f(s), so that simple approximations to the integrals in exp. (1) can be derived (e.g. [K.V.Horoshenkov et al, JASA, 104, (1998)]) If Pade approximation fails, an alternative can be 1. Interpolate the experimental data on the cumulative pore size distribution 2. Numerically differentiate the result to obtain the experimental PDF e(s) 3. Carry out direct numerical integration of exp. (1) 32

33 COUSTONE (Flint mixed with epoxy resin binder) R = 31.5 kpa s m -2, Ω =0.40, q 2 = 1.66, h = 21mm 10mm 33

34 The normalised surface impedance of a 20 mm layer of Coustone (predicted from the pore size distribution data) 34

35 What are common complications in modelling acoustic properties of porous media? 35

36 Loose granular media in different compaction states 36

37 Effect of particle size 40mm thick layer 1.0 <0.15 mm mm mm Sound absorption coefficient mm mm mm mm mm greater particle size Frequency, Hz 37

38 Criteria for improved model for loose granulates A general and more simple method is to relate empirically the acoustic properties of a loose granular mix to the following parameters: characteristic dimension of the particles porosity specific density of the grain base. These parameters are directly measurable in-situ and can account phenomenologically for: the degree of compaction viscous effects microporosity particle friction. 38

39 An improved semi-empirical model 1. Relates the characteristic dimension of the particles and accounts for the viscous effects in the porous structure via characteristic particle dimension χ = Dρ c 0 10 η 4 density of air sound speed dynamic viscosity 2. Accounts phenomenologically for the particle micro-porosity and frame vibration effects via M = ρ g 3 10 ρ 0 specific density of gains 39

40 Acoustic Properties It can be shown that the characteristic impedance (W) and propagation constant (γ) can be expressed empirically W = f( Q, χ, M) and some analytical functions γ = gq (, χ, M) where the structural characteristic is also predicted empirically by Q = wavenumber 0.2(1 Ω )(1 +Ω) Ω kdχ 2 porosity 40

41 Results for real part of characteristic impedance acoustic resistance Voronina and Horoshenkov, Appl. Acoust., 65, (2004) 41

42 Results for real part of propagation constant Voronina and Horoshenkov, Appl. Acoust., 65, (2004) 42

43 Effect of moisture tested sample funnel 43

44 Resistance Effect of moisture on the impedance of a 50mm water-saturated layer of fine sand 140 S = 94% S = 72% 80 z s 60 S = 48% S = 29% S = 19% S =13% S = 0% Frequency, Hz

45 Effect of double porosity (macro-perforation) micro-porous frame macro-pores l / l > 10 from F. Sgard and X. Olny, Appl. Acoust., 66(6), p m 45

46 Homogenisation procedure for double-porosity media Porosity Dynamic density Ω =Ω + (1 Ω ) Ω db p p m {(1 ) / 1/ } 1 ρ = Ω ρ + ρ db m p Complex compressibility { (1 ) } C = C + Ω C db p p m The key point is linked to the fact that the wavelength in the microporous domain should be of the same order of magnitude as the mesoheterogeneities, i.e. the characteristic frequency of pressure diffusion effects is carefully chosen ω ω characteristic frequency of pressure diffusion effects (1 Ω ) P ρ d = p 0 0 D(0) Ω 2 R 2 v m m q 2 m 1 characteristic viscous frequency 46

47 Effect of double porosity (macro-perforation) on absorption properties from [Sgard and Olny, Appl. Acoust., 66(6), 2005]. 47

48 A realistic double porosity structures developed at Bradford ~7mm 48

49 Finally! Effect of frame vibration 49

50 Measured absorption coefficient of G10 plates 500mmx500mm and 90mm with 80 mm air gap [Swift and Horoshenkov], JASA 107, (2000). 50

51 Basic equations Biot coupling coefficient loss coefficient P. Leclaire, K. V. Horoshenkov, et al, JSV 247 (1): (2001). 51

52 Predicted effect of material density on the averaged absorption coefficient (a 10mm thick plate 80 mm from rigid impervious wall) 52

53 THANKS FOR YOUR ATTENTION 53