Validation of Micro-Perforated Panels Models

Transcription

1 Purue Universiy Purue e-pubs Publicaions of he Ray W. Herrick Laboraories School of Mechanical Engineering Valiaion of Micro-Perforae Panels Moels J Suar Bolon Purue Universiy, bolon@purue.eu Kang Hou Follow his an aiional works a: hp://ocs.lib.purue.eu/herrick Bolon, J Suar an Hou, Kang, "Valiaion of Micro-Perforae Panels Moels" (008). Publicaions of he Ray W. Herrick Laboraories. Paper 100. hp://ocs.lib.purue.eu/herrick/100 This ocumen has been mae available hrough Purue e-pubs, a service of he Purue Universiy Libraries. Please conac epubs@purue.eu for aiional informaion.

2 Valiaion of Micro- perforae Panels Moels Kang Hou J. Suar Bolon Ray W. Herrick Laboraories ao Purue Universiy

3 Ouline Moels for he Micro-perforae Panel Maa Moel Moifie Maa Moel FEM Moel (base on rigi porous frame) Avance for Impeance Tube Four Microphone Impeance Tube Measuremen Error Analysis & Calibraion Proceure Resuls & Conclusion Fuure Work Moifie FEM Moel Elasic Porous Frame

4 Inroucion o he MPP & Maa Moel Environmenally frienly Goo low frequency performance Afforable in he recen! Classical l Maa Moel (1998) No Flexural Moion No hole ineracion Resisive Uneresimaion Classical MPP Moels MPP Moels Valiaion Maa Moel (1975, 1987, 1998) Allar s Moal Approach Beranek/Ingar Moel Analyical~Maa Moel (1987) Numerical~Finie Elemen Meho Experimenal~Four Microphone Impeance Tube 3

5 Moifie Maa Moels P 1 En correcion P Shearing region MPP Impeance Z 1 z r jm c Z 1 : specific acousic impeance : porosiy 0 r : resisance m: effecive mass per uni area x: perforaion consan 3 r c ( x 1 3 Conribuion from hole m (1 c c 1 9 x x ) 8 En correcions 0.85 ) 1 3 Accoun for he hole ineracion 1.5 Moifie 1987 Version Base on Ingar s semi-empirisic formula for perforae panels Inrouce consan parameer o moify he resisive en correcion 4

6 Absorpion Coefficien & Transfer Impeance Absorpion Coefficien Transfer Impeance Numeric Error 4r n L ( 1 r) m co c Resisive par eermines absorpion peak locaion Reacive par eermines absorpion peaks heigh -Microphone & 4-Microphone A sraighforwar way o invesigae he maerial impeance Avoi he numeric error Speaker 5

7 Finie Elemen Moel Johnson-Allar Moel Sofware Simulaion Equivalen Toruosiy MPP 3 1 e 0.48 r ( ) e Rigi Porous Maerial : porosiy : flow resisiviy : viscous char lengh : hermal char lengh : equivalen oruosiy Parameers Require All he exising moels can be obaine from an equivalen flui moel by selecing he appropriae parameers Finie Elemen Moel Impeance Tube 6

8 Recen Developmen for he Impeance Tube Sanar Two Microphone Impeance Tube Measuremen Four Microphone Impeance Tube Measuremen ISO ASTM E 1050 beer suie for exracion of maerial properies complex wave number complex characerisic impeance P ( AB) jk jk x0 x jk jk ( ) x0 0 ( ) x 0 V A B c P V x0 T T 11 1 P ( Ce De ) V Ce De c T T 1 P V x T T cosk 11 1 p T1 T j sin kp / p c Transfer Impeance Z p P0 V0 P V j pcp sinkp cos kp 7

9 Non-Swiching Approach Error Sources Microphone Mismach Bias Error Tube Aenuaion Single microphone moves o locaion 1,,3,4 Correce facor H c 1 ( H I H ) 1/ Correce ransfer funcion ~ 1 H 1 / H c 1 H For low ransmission loss maerials, phase mismach is major concern Non-Swiching approach can avoi phase mismach phenomenon Accuracy epens on he saionary of elecronic sysems an FFT average 8

10 Experimen Seup Tese Maerial: Brass Sample Harware: B&K Type 406 (.9cm iameer) Sample Diameer Hole Deph Porosiy Number [mm] [mm] φ[%] Sofware: COMET/ACOUSTICS-SAFE 9

11 Resuls-Low Perforaion Rae Maa Moel uneresimae resisive par of he impeance in low perforaion rae case FEM moel is accepable The highlighe peak comes from he flexural panel vibraion 10

12 Resuls-High Perforaion Rae Maa moel overesimaes he reacance ue o neglec of hole ineracion Improve Maa Moel gives he bes mach wih experimenal resuls 11

13 Conclusion Analyical, numerical an experimenal resuls for micro-perforae brass panels were compare An improve Maa moel was propose o ake ino accoun hole ineracions an moificaion of en correcions An improve impeance ube measuremen was se o give more accurae experimenal resuls 1

14 Fuure Work Furher experimen shoul be aken o correc he equivalen oruosiy in he FEM moel I s possible o use FEM o ake ino accoun he flexural vibraion of MPP FEM moel also has he poenial o be use in he complicae srucures res 13