Sound Absorption Characteristics of Membrane- Based Sound Absorbers

Transcription

1 Purdue e-pubs Publicatis f the Ray W. Schl f Mechaical Egieerig Sud Absrpti Characteristics f Membrae- Based Sud Absrbers J Stuart Blt, blt@purdue.edu Jih Sg Fllw this ad additial wrks at: Blt, J Stuart ad Sg, Jih, "Sud Absrpti Characteristics f Membrae-Based Sud Absrbers" (2003). Publicatis f the Ray W.. Paper This dcumet has bee made available thrugh Purdue e-pubs, a service f the Libraries. Please ctact epubs@purdue.edu fr additial ifrmati.

2 Segwip, Jeju, Krea August 25-28, 2003 Sud Absrpti Characteristics f Membrae-Based Sud Absrbers August 28th, 2003 Jih Sg ad J. Stuart Blt Ray W.

3 Mtivati Recetly, it has bee bserved that Macr-cellular plylefi fams (e.g.,quash-like) absrb sud eergy eve thugh h the fams are mstly clsedcelled ad the average cell size is very large. * Hw des this sud absrpti arise? Hw d yu mdel this effect? * C. Park et al., New Sud-Absrbig Fams frm Plylefi Resis, Prc. f Iter- Nise 2000, pp , 2000

4 Quash Membrae Mdel - T this pit, mdel is based tesied membraes - Stiffess f this mdel is prvided by tesi f membrae Tp View f Quash Membrae Tesi

5 Fam Mdelig Prcedure 3-D Mdel 2-D Mdel Sud Eergy Lss Mechaisms Eergy dissipati by membrae flexure Viscus lss thrugh perfrati Uit cell Membrae Rigid Frame Material Prperties Tesi Lss factr Membrae Desity Surface Film Desity Prsity Flw Resistace Therm-viscus budary layer effect

6 Theretical Mdel - Permeable Membrae I INCIDENT WAVE REFLECTED WAVE FLUID II TRANSMITTED WAVE Assumed Slutis TENSIONED, PERMEABLE MEMBRANE Sud Pressures i Acustic Cavities: P ( k r) e P jkz I( r, z) e B J II( r, z) CJ ( k r) e Membrae Displacemet (Slid Cmpet): y (, ) A J ( 0 ) Membrae Displacemet (Fluid Cmpet): ( r, t) F J ( k0 r r jk u r) F z z jk z z

7 Theretical Mdel Sluti Methd Budary Cditis - The Ctiuities f Velcity at the Bth Side f a Membrae: 1 PI y u (1 ) j z z t t 0 1 PII y u (1 ) j z z0 t t Sluti Methd Apply fur budary cditis a pit-by-pit basis acrss the membrae Particle Psiti I II r - The Frce Equilibrium Equati i the Membrae: 2 2 R s y f y 2 T t T where ( y u) (1 ) ( PI P t T 2 u ( y u) h R ( P I P 2 t f t 2 T T (1 j) N a / A ( II ) P frt II ) P back R f v f y A1 ~... A N B 0 Cefficie t... B N Matrix C 0... C N Number f Pit at which B.C. s applied Frcig Vectr

8 Eergy dissipati by Membrae INCIDENT WAVE REFLECTED WAVE TRANSMITTED WAVE Measuremet Sud Pressure frm micrphes Estimati Furier Bessel ceff. f Icidet / Trasmitted Waves Nrmal Icidet Reflecti ceff.: R MEMBRANE Trasfer Impedace f Membrae : Z m = (1+R) / (1-R) -ρ c

9 Trasfer Matrix Methd Membrae & Air Cavity Trasfer Matrix T m = 1 0 Z m Ttal Trasfer Matrix P Tp = utp 1 u T ttal P u Reflecti Cefficiet Absrpti Cefficiet Bttm Bttm a T = R Tp cs( ( k ( l 2 l1 )) i c si( k ( l 2 l1)) m s ic si( i( k ( l 2 l1 )) cs( k ( l 2 l1)) T T T T T Z Z ttal Tp Tp = c c 1 RTp 2 T a 1 layer m a N layers 1 layer m N layers T a

10 Experimetal Set-up Pwer Amplifier B&K Pulse System Sigal Aalyzer Pre-Amplifier Cmputer Sud Surce Micrphe Stadig Wave Tube Quash Sample

11 Experimetal Set-up Ladig gquash Sample Measuremet Set-up

12 Cmparis f Measuremet ad Predicti m = kg/m 2, T =0.13 N/m, =1.6, m s = kg/m 2, Ω=0.0085, R f =0.286 Rayls, t= m, d = m, h= m, N=12 12.

13 Parameter Effects Sud Absrpti Fam Thickess Membrae Size m =0.07 kg/m 2, T=0.5 N/m, =0.7, m s =0.2 kg/m 2, m =0.07 kg/m 2, T=0.5 N/m, =0.7, m s =0.2 kg/m 2, Ω=0.01, 01 R f =0.2 Rayls, t= m, d = m, Ω=0 0.01, 01 R f =0.2 2Rayls, t= m, N=10

14 Parameter Effects Sud Absrpti Surface Mass Membrae Prsity m =0.07 kg/m 2, T=0.5 N/m, =0.7, Ω=0.01, m =0.07 kg/m 2, T=0.5 N/m, =0.7, m s =0.07 kg/m 2, R f =0.2 Rayls, t= m, d = m, N=10 R f =0.2 2Rayls, t= m, d = m, N=10

15 Parameter Effects Sud Absrpti m s = kg/m 2, Ω=0.0, R f =0.2 Rayls, t= m, d = m, h=0.056 m, N=12 (1/3-ctave bad rmal icidece absrpti averaged frm 125 Hz t 1600 Hz)

16 Sme High Absrpti Desigs New Desig k m = kg/m 2 ( ), T =0.065 N/m ( ), =1.6, m s = kg/m 2 ( ), Ω=0.02( ), R f =0.286 Rayls, t= m, d = m( ), h= m, N=10( ) New Desig 2 m = kg/m 2 ( ), T =0.13 N/m, =1.6, m s = kg/m 2 ( ), Ω=0.03( ), R f=0.286 Rayls, t= m, d = m( ), h= m, N=10 ( )

17 Cclusis & Future Wrk A acustical mdel fr membrae-based sud absrbig materials was preseted ad was verified experimetally the basis f acustical measuremets. It has bee fud that the theretical mdel ca accurately reprduce the acustical behavir f the particular fam studied here. It was shw that the chice f particular cmbiatis f material prperties ca result i imprved sud absrpti. The preset wrk ca prvide the fudati ecessary t desig membrae-based sud absrbig materials havig ehaced sud absrpti capacity. The preset wrk implies that alterative stiffess mechaisms f membrae systems such as flexural stiffess, membrae curvature, bulk elasticity, ad membrae ihmgeeity, ca als result i sud dissipati i membrae-based fams; this wrk will be preseted i the future.