The Effect of Flexibility on the Acoustical Performance of Microperforated Materials

Transcription

1 Purdue University Purdue e-pubs Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering -- The Effect of Flexibility on the Acoustical Performance of Microperforated Materials J Stuart Bolton Purdue University, bolton@purdue.edu Jinho Song Taewook Yoo Ryan Schultz Yangfan Liu Follow this and additional works at: Bolton, J Stuart; Song, Jinho; Yoo, Taewook; Schultz, Ryan; and Liu, Yangfan, "The Effect of Flexibility on the Acoustical Performance of Microperforated Materials" (). Publications of the Ray W. Herrick Laboratories. Paper 6. This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information.

2 J. J Stuart Bolton Ray W. Herrick Laboratories School of Mechanical Engineering Purdue University With thanks to: Jinho Song (Otis Elevator), Taewook Yoo (3M/EAR) (3M/EAR), Ryan Schultz (Sandia) and Yangfan Liu (Purdue) ASA Fall F ll meeting, i K Kansas City, Ci //

3 Micro-perforated film in a modular, tile-based design Installed in exhibit Absorption performance

4 Solid phase of microperforated materials having superficial densities less than 5 g/m may be driven into motion by the incident sound field (direct pressure + viscous drag) Energy is dissipated by flexure of the solid phase and relative motion of the fluid in the pores and the solid phase motion of the solid phase affects this process Two extremes considered here: membrane like performance modified by porosity; rigid microperforated performance modified d by flexibility of the solid phase 3

5 Solution Method Apply two velocity continuity boundary conditions and membrane equation of motion on a point-by-point basis across the membrane Particle ce Position System Response (Membrane Displacement) Membrane Displacement I II r ~ Number of Point at which B.C. s applied y Matrix A 6 Membrane Displacement (Top View)... A B... B C... C N N Coefficien t = N forcing Vector Frequency[Hz] Frequency[Hz] Radius[m] Radius[m] 4

6 5

7 Vibrational Modes Theory Experiment Absolute velocity of membrane - Experiment Phase st v/p / v/p max.5.5 y x v/p / v/p max y x.5.5 Magnitude.5 Phase y y x x Absolute velocity of membrane - Experiment Phase nd p / v/p max v/p.5.5 y x v/p p / v/p max y x.5.5 Magnitude.5 Phase y y x x 6

8 Power Amplifier Pre- Amplifier Signal Analyzer Microphone Sound Source Anechoic Termination Test Sample 7

9 Given experimental results as input, Find appropriate material properties (T o, ρ s, η ) TL T 8Pa. 4 s.87 kg m Note : Mass law trend with large peaks associated with zero volume velocity modes 8

10 Membrane with finite-depth backing space Imaginary part of Impedance Absorption Coefficient Many resonances because of membrane dynamics Z n Z n, Membrane Z n, Backing Frequency [Hz] T 75 Pa. 63 kg s.9 m l.9 m Frequency [Hz] - Absorption peaks when Im{ Z n } = - Significant sound absorption in narrow frequency regions produced by dissipation in the membrane 9

11 Assumed Solutions Sound Pressures in Acoustic Cavities: P ( k r) e jkz I( r, z) e Bn Jo n PII( r, z) CnJ o n r r n ( k r) e Membrane Displacement y ( r, t ) A J ( k r n o ) n (Solid Component): n n jk z n jk z z n z Membrane Displacement (Fluid Component): u( r, t) Fn J o( k r) n n

12 A duct with a tensioned, permeable membrane Increasing Porosity Membrane Each pore had a diameter of approximately.5 mm and the total number of pores ranged from 4 to increasing in steps of 4: the pores were uniformly distributed over the membrane. Flow resistance controls background level of energy dissipation

13 Sound Power Dissipation from Membrane Sound Power Dissipation from Fluid a=.5 m, s =.74 kg/m, T o =85 N/m, =.5, Ω=.8, h=. mm Viscous energy dissipation i i controlled by flow resistance of membrane

14 Relatively heavy (>3 g/m ), not tensioned but flexurally stiff Advantages over fibrous material o stiffness (self supporting), robust, weatherproof Energy dissipates when sound moves through small holes o d=.~.9 mm, t=.~ mm, N= 3 ~ 6 per m Front side crosssection 3

15 Volume velocity continuity at x= j o pi x x d ( ) t s d f t pii j x o x d d d d s ( ) t t Force equilibrium at x= ( d f ds ) 4 d Solid pi pii Rt D ds T ds s t t Fluid p I p II ( d R t f d t s f ) d f joh' t s p I : Pressure at source side p II : Pressure behind the panel d s : Displacement of solid part d f : Displacement of fluid part ρ s: Membrane mass per unit area R f : Flow resistance D: Flexural stiffness T: Tension h : : Effective thickness Ω: Porosity 4

16 3-dimensional model P P Sound pressure in each region jkx I e Bmn cos( kmz)cos( kn mn jk II Cmn cos( kmz)cos( kn y) e mn y) e xmn jk x xmn e jk x xmn ( xl) Only symmetric modes exist k m m n kn Lz Ly (m, n=,,, ) Displacement of membrane k x j k k k k m m k k mn n n (k>k n +k m ) (k<k n +k m ) for simply supported BC Solid part Fluid part d d s f m n m n A F mn mn sin cos k z sin k y m k zcosk y m n n for clamped BC Solid part Fluid part d d A cos k z cos k y s mn m n mn f mn F mn cos k zcosk y m n k m z m L, k n y n L (m, n=,, ) 5

17 Sample (x) Sample (x5) Sample 3 (x5) d (nominal) t ρ s [kg/m ] Sample Sample Sample cm by 6.5 cm N 6

18 Rigid perforated behavior slightly modified by flexibility n S n S d (nominal) d (adjusted).4.3 prediction B.D.= cm measurement B.D.= cm. prediction B.D.= cm measurement B.D.= cm. prediction B.D.=4 cm measurement B.D.=4 cm Freq [Hz] t S S S D / loss factor [N m ].7/.7.7/.7.7/.7 T [N] ρ s [kg/m ] N n.4.3 prediction B.D.= cm measurement B.D.= cm. prediction B.D.= cm measurement B.D.= cm. prediction B.D.=4 cm measurement B.D.=4 cm Freq [Hz] S3.3 prediction B.D.= cm measurement B.D.= cm. prediction B.D.= cm measurement B.D.= cm. prediction B.D.=4 cm measurement B.D.=4 cm Freq [Hz] 7

19 d t D [N m ],.6,.4,.3,.,.,.,. loss factor in D T [N] Mass/area [kg/m ] N Size x 63.5 Depending on the flexural stiffness, the absorption performance can be enhanced with an appropriate loss factor Absorption bandwidth can be increased Performance is reduced if stiffness is too low n D= D= D=.4 D=.3. D=. D=.. D=. D= Freq [Hz] 8

20 n B] TL [db Freq [Hz] Freq [Hz] Hz Hz 5 Hz d t D [N m ] loss factor T [N] ρ s [kg/m ] N Size x

21 P I P II W I * Re P u dydz I I z y W II * Re P u dydz II II From sound fields W E.D._field = W I - W II W W * 4 d ( d f ds) ds Re s D d s T ds s Rt dydz t t t * ( d f d s ) d f df Re R dydz t joh t t t E. D._ solid E. D._ fluid ' From displacements of solid and fluid parts W E.D._disp. =W E.D._solid + W E.D._fluid. W E.D._field = W E.D._disp.

22 4.5 5 x -6 4 W W W E. D. field.5 x -6 Dissipated Energy [W W] Dissipated Energy [W] x Freq [Hz] -6.5 W E. D. field W E. D. disp Freq [Hz] Dissipated En nergy [W].5.5 Power of solid Power of fluid Power of solid + fluid parts Freq [Hz] d t Number of holes per unit area Mass/area [kg/m ] Tension / loss factor Flexural Stiffness/ loss factor Panel size , / x 63.5 mm

23 . Very lightweight tensioned, permeable membranes acts like impermeable membranes, but energy dissipation (and absorption) can be increased by control of porosity and flow resistance. Relatively heavy, flexurally stiff, microperforated materials act essentially like rigid microperforated materials but additional absorption features attributable to flexing of the panel appear, and can increase absorption bandwidth if stiffness is not too low 3. Energy dissipation by flexure of the microperforated panel can be comparable to the energy dissipation due to viscous losses in the pores

24 . Ryan A. Schultz, J. Stuart Bolton, Jonathan H. Alexander, Stephanie B. Castiglione, Tom P. Hanschen and Ed Bronikowski, Improving the visitor experience a noise study and treatment design for the Smithsonian National Zoological Park s Great Ape House, Proceedings of INTER-NOISE, 8 pages,.. Jinho Song and J. Stuart Bolton, Modeling of membrane sound absorbers, b Proceedings of INTER-NOISE, paper N574, 6 pages, Dearborn, Michigan, August. 3. Jinho Song and J. Stuart Bolton, Acoustical modeling of tensioned, permeable membranes, Proceedings of NOISE-CON 3, paper nc3_, 6 pages, Cleveland, Ohio, June Taewook Yoo, J. Stuart Bolton, Jonathan H. Alexander and David F. Slama, Absorption of finite-sized micro-perforated panels with finite flexural stiffness at normal incidence, Proceedings of NOISE-CON 8, Dearborn, Michigan, July 8-3, 8. Presentations ti available at Herrick Labs epub site: 3