Acoustics Field and Active Structural Acoustic Control Modeling in ANSYS

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1 Acoutc Feld ad Actve Structural Acoutc Cotrol Modelg ANSYS M. S. Kha, C. Ca ad K. C. Hug Ittute of Hgh erformace Computg 89-C Scece ark Drve #0-/, he Rutherford Sgapore Scece ark, Sgapore 86 Abtract: h artcle attempt to exame acoutc fte elemet aaly coupled wth tructure, ad provde the eceary formato to apply ANSYS for a wde cla of tructural acoutc problem. Frt part of th artcle decrbe the acoutc feld ad hece the ue of acoutc pot ource ANSYS. Reult are explaed ad compared wth that of aalytcal oluto. Ad ecod part deal wth the actve cotrol of tructural acoutc problem. Reult are preeted for global cacellato of a prmary moopole' oud feld by the ue of multple pezoelectrc elemet boded to the urface of the elatc tructure to provde cotrol force. Itroducto: A we kow, ANSYS ca be appled to carry out the acoutc aaly, whch clude the geerato, propagato, catterg, dffracto, tramo, radato, atteuato, ad dpero of oud preure wave a flud medum [, ]. I the ANSYS/Multphyc ad ANSYS/Mechacal program, a acoutc aaly uually volve modelg the flud medum ad the urroudg tructure. he ANSYS program upport a harmoc repoe aaly due to harmoc exctato, a well a modal ad traet acoutc aalye. he ormal procedure clude four major tep a harmoc acoutc aaly: buld the model, apply boudary codto ad load, obta the oluto ad revew the reult. Oe of the purpoe of th paper to addre the acoutc feld modelg durg the model creato ad the flow-type load applcato whe coderg the oud catterg ad reflecto problem. Actve cotrol of tructural acoutc ha bee a great teret to the reearcher the recet year. ezoelectrc ubtace uch a Z ha the ablty to cotrol acoutc feld by the troducto of electrc feld or voltage potetal. Few FEA package are avalable where pezoelectrc materal trogly coupled wth flud medum ca be cluded drectly for the purpoe of actve cotrol. h paper wll alo how the ablty of ANSYS to exame the global reducto of the radated oud preure a harmocally excted ecloed flud medum, where pezoelectrc materal wll be ued a the cotrol force. Acoutc Flud-Structure Couplg: For the coupled flud-tructure teracto problem, the flud preure load actg at the terface added to the tructure equato of moto a follow, M 0 0 u&& C + 0 && 0 0 u& K + 0 & Z K Z u pr K F + F d K L () Where, M Structural ma matrx C Steructural dampg matrx K Structural tfe matrx

2 d K delectrc coductvty matrx z K pezoelectrc couplg matrx F tructural load vector (vector of odal force, uface force ad body force) L electrc load vector, appled odal charge vector pr F flud preure load vector he flud preure load vector at the terface S obtaed by tegratg the preure over the area of the flud/tructure terface urface. F pr { N } { } ds () N } Where { are the hape fucto employed to dcretze the dplacemet compoet u, v, w (obtaed from the tructural elemet), {} the ut ormal to flud/tructure boudary. Detal of fte elemet formulato of flud tructure couplg alog wth the pezoelectrc aaly ca be foud referece [3]. Acoutc Feld: he theoretcal model uderlyg all mathematcal model of the acoutc propagato the wave equato. he wave equato derved from the more fudametal equato of tate, cotuty ad moto. he aumpto made acoutc ad flud-tructure aalye are that the flud behave a a deal acoutc medum. h mple that () the flud otropc ad homogeeou, () thermodyamc procee are adabatc, () the flud vcd (o vcou dampg), ad that (v) acoutc preure ad dplacemet ampltude are mall relatve to the flud ambet tate. he acoutc wave equato gve by p p c t where, c the acoutc wave peed. c κ/ρ. ρ the flud dety, ad κ the flud bulk modulu. h paper wll ot dg to the fte elemet formulato of tructural acoutc. Detal of fte elemet formulato of the wave equato ca be foud referece [,3]. Apply flow-type load o the model: (3) here four load type acoutc aaly of ANSYS: cotrat (dplacemet, preure); force (force, momet, flow loadg); urface load (preure mpedace, flud-tructure teracto flag) ad erta load (gravty, pg, etc.). Geerally, t traghtforward work to pecfy the load o the FEM model except for the flow loadg whe applyg a acoutc loadg at a ode the acoutc medum. How to terpret the phycal cocept of the flow-type ource crucal for u to apply t a correct way. Soud preure feld D acoutc problem: It foud that the flow-type acoutc ource the ANSYS -dmeoal acoutc aaly behave a a pulatg cyldrcal ource whe the elemet behavor et to be plae tra. Suppoe that we have a log cylder of radu a, whch expadg ad cotractg uformly uch a maer that the velocty

3 t of the urface of the cylder v e ω. he acoutc feld cloe to the ource complcated, but a mple expreo ca be obtaed the far feld approxmato. he preure ad velocty at large dtace from the pulatg cyldrcal oud ource are [4] p π ρ a cf k (r e r + π ct) - 4 (4) ν π a f k (r e cr + π ct) - 4 where r the dtace from the ource to the obervg pot. k the wave umber, whch equal to ω/c. ω the crcular frequecy. c the oud peed ad f the frequecy. ρ the ma dety of acoutc medum. he flowg load provded the ANSYS mulated ug effectve flud load [] a u F -Aρ & Qρ t where A a repreetatve area aocated wth the flowg ource. u the outward ormal dplacemet of flud partcle to the urface of a flud meh. Q && the volume accelerato. From equato (6), t ee that the flowg load actually a product of the volume accelerato ad medum dety. herefore, we have the volume accelerato expreo a for a gve cyldrcal flow ource wth radu of a ad legth of l: t Q& ω πalωe (5) (6) (7) So the partcle velocty cloe to the ource wll be, f the flow ource F gve: F ωt v e πalωρ (8) For plae tra problem, we may make t be oe, Hece the velocty ampltude term F πaωρ For preure ampltude oly, equato (4) ca be wrtte a (9) F p ω fc kr + ωt α e e e r (0) or ρ Q&& ω fc kr + ωt α e e e r () Equato (0) decrbe the relatohp betwee a flow-type ource, pecfed ANSYS ad the preure feld geerated by the ource at far feld.

4 Le ource coted of cyldrcal ource: he oud preure feld geerated by a le ource (legthl) cotg of the cyldrcal ource for far feld ca be decrbe a [5] p ( r θ ) ( klcoθ ) ρq&& c π kr ωt, L e e e pc 0 4π fr klcoθ 4 θ () r j ( klco ) () ρq&& c π kr ωt 4 where pc () r L e e e the preure feld radated from a magary cyldrcal 4πr fr ource free pace located at the org whoe volume accelerato that of the whole le ource. j o the phercal Beel fucto. Soud feld radated by a cyldrcal pot ource wth a fte rgd boudary: he oud feld the half pace bouded by a rgd baffle ca be decrbed a [5] p ρq&& πr ke R e R kr ωt ( r, θ ) e co( kecoθ ) e,, << (3) where e the dtace of ource from the baffle ad R the radu of the boudary. Global reducto of D catterg oud preure: A two-ed mply upported blamated plate, whch compoed of a elatc layer cotact wth the flud, ad a pezoelectrc layer, loaded wth half-pace flud (water) ha bee codered for global catterg oud preure problem. he elatc ad pezoelectrc layer are perfect cotact, ad the terface betwee the two a electrode of eglgble thcke, whch ca produce a voltage dfferetal acro the pezoelectrc layer. he pezoelectrc layer aumed to be polarzed the drecto ormal to the elatc/pezoelectrc terface, ad compoed of Z4. he dmeo of the elatc ad pezo layer are of m x 0.0m ad m x 0.0m repectvely. Fgure how the chematc of the problem decrbed above. he flud medum ha bee cotructed by a half crcle of radu, r 3m, from the ceter of the plate. Source tregth, F00 kg/ec, whch decrbed the prevou ecto, ha bee choe for th cae. Fgure - Sketch of catterg preure reducto problem

5 he fte acoutc elemet (FLUID9) ued alog the crcular boudary ca aborb the preure wave whch mulate the outgog effect of a doma that exted to fty beyod the acoutc feld modeled by fte elemet of FLUID9. FLUID9 provde a ecod-order aborbg boudary codto o that a outgog preure wave reachg the boudary of the model aborbed wth mmal reflecto back to the flud doma. he fte elemet perform well for low a well a hgh frequecy exctato. It tate that the placemet of the aborbg elemet at a dtace of approxmately 0.λ beyod the rego occuped by the tructure or ource of vbrato ca produce accurate oluto. Here λ the domat wavelegth of the preure wave. For example, the cae of a ubmerged crcular or phercal hell of dameter D, the radu of the eclog boudary hould be at leat ( D + 0.λ). 0 elemet per wavelegth have bee take for each cae. he plate tructure excted wth the flow ource at x -0.4m, y 0.4m. Uder the preure radated by the ource oe, the plate wll vbrate ad radate oud to the upper half-pace flud medum. he oe level at ay pot the feld deped o the properte of the pot ource (prmary ource) ad the cotrol force (ecodary ource) appled at each pezoelectrc elemet. For a gve et of actuator, the cotrol force that mmze the average acoutc repoe ca be ealy calculated by complex LMS algorthm. Method for choog locato of the actuator eeded. Objectve fucto of the optmzato trategy to mmze the um of quared preure at the feld ode. Uder the aumpto of uperpoto, the total radated oud preure geerated the feld ca be tated a the um of oud preure due to the prmary ource ad the cotrol force. t + c (4) where t the total oud preure the oud preure created by pot ource c the oud preure geerated by pezoelectrc elemet Matrx form of th preure equato a follow, { } [ A] { X } + { } (5) t,, L L,, where { t } vector of total oud preure at ode [A] trafer fucto matrx, whoe colum are compoed of the oud preure compoet cotrbuted by the ut voltage of dfferet pezo elemet. {X} vector of dered voltage at dfferet pezo elemet { } vector of calculated oud preure at dfferet ode the area of cocer wth o actve cotrol. o. of ode the area of teret. L o. of pezo electrc elemet ued for the cacellato problem. o acheve dered reducto of oud preure t eceary to kow the relatohp, trafer fucto matrx A equato (5), betwee the force (or appled voltage) of each pezoelectrc elemet ad the oud feld geerated by the pezoelectrc elemet. herefore, we make ue of the fully acoutcpezoelectrc-mechacal coupled fucto provded by the commercal FEM code: ANSYS. he trafer fucto matrx A developed by calculatg the oud preure feld due to the ut ampltude of appled voltage the every gle pezoelectrc elemet leavg the other elemet hort-crcuted ad thu the

6 colum of trafer matrx A ca be compred eparately. Implct form of the above metoed matrce are a follow: M, L cl c c L cl c c L cl c c ) ( ) ( ) ( () () () () () () L M O M M L L A, (6) L M X o reduce the preure feld, whch produced by the prmary ource, the objectve fucto to be mmzed for the optmzato purpoe choe a the um of the quared preure over the ode (), whch repreet the repoe feld. ( ) ( ) t t o * 7) ( Where * the complex cojugate. he cot fucto, whch wll be checked durg the optmzato, ca be wrtte o a decbel cale to compare the global preure wth ad wthout cotrol. A egatve reult the cot fucto repreet a decreae oud preure level caued by the Z actuator. (8) 0 log0 co * * t t t he leat quare approach ha bee ued th work to etmate the requred voltage at every pezo electrc elemet to cacel out the oud preure at a pecfed area of teret. { } [ ] { } { } ) (9,,,, L L X A E where {E} the vector of error term. If L, the the voltage the dfferet pezo elemet would be uquely determed wth {E} 0 ad equato (5) beg olved for {X} by drect vero. he method of leat quare ued to determe the voltage {X}. For that, ( ) E to be mmzed. he mmzato preeted by ( ) (0) 0 j X E where X j the jth compoet of {X}. Note that

7 { E} { E} ( E ) { E } { E} { X } [ A] [ A]{ X } { X } [ A] [ ] + { } { } Mmzg th wth repect to {X} (equato (7)), t may be how that: {} 0 [ A] [ A]{ X } [ A] [ ] or [ A ] [ A]{ X } [ A] { } () Fally, ( ) [ A] { } () { X } [ A] [ A] For a gve et of L actuator, the force X whch mmze the ether equato (7) or (8) ca be calculated by olvg the complex leat-quare equato (). Reult ad Dcuo: he prmary goal of th tudy to model acoutc feld ad hece to mplemet actve cotrol ug pezoelectrc elemet wth the help of coupled feld aaly of FEM oftware, ANSYS. Frt, acoutc feld geerated by pot ource ad le ource wll be dcued for a free flud medum of radu m, ad the the fluece of the dtace of the pot ource from the baffle wll be dcued. Fally, a cae of global reducto of oud preure ad tructural vbrato ug multple pezoelectrc elemet boded to the elatc tructure ecloed by a flud medum of radu 3 m wll be demotrated. wo-dmeoal problem ha bee choe for the cae tude. he fte elemet model ued a ymmetrc old half-crcle of radu m, flled wth acoutc flud elemet ad a fte acoutc radato boudary ha bee defed alog the crcular boudary. Cyldrcal ource of tregth of 00 kg/ec have bee choe for all cae f ay. Harmoc aaly performed wth a fxed frequecy of 5 khz. Fgure ad 3 how the preure feld geerated by a pulatg cyldrcal ource (moopole) va aalytcal calculato (equato 0) ad FEM mulato repectvely. It oberved that there a good agreemet betwee two reult. Fgure - reure at fte boudary for moopole ource

8 Fgure 3 - reure cotour for moopole ource Fgure 4 to 7 how the preure feld geerated by two cyldrcal ource ad t accuracy depedece o the pacg betwee two ource. It otced that the devato of the drectvty patter become obvou wth the creae of the ource pacg. It becaue there ext a requremet whe applyg the fte boudary elemet, whch aborb the wave that are outgog. It cocluded that the ceter of the boudary crcle hould be a cloe to the ceter of the model a poble. Fgure 4 - reure at boudary for dtace betwee ource of 0.4 m

9 Fgure 5 - reure cotour for dtace betwee ource of 0.4 m Fgure 6 - reure at boudary for dtace betwee dpole ource of.6 m

10 Fgure 7 - reure cotour of dpole ource for dtace betwee ource of.6 m A mple cae of cotuou le ource coderg a dtrbuto of cyldrcal ource alog the le ha bee employed to clarfy further the ANSYS reult wth that of aalytcal oe. he ear feld acoutc feld (r,θ) of a cotuou le ource of legth L (m), dtace betwee the ource of 0.0m, foud by ummg the cotrbuto of the mple cyldrcal ource degated alog the le. Fgure 8 how the preure ampltude at the crcular boudary, cetered at the ceter of the le, of radu m. ANSYS reult how exact value lke the aalytcal reult where mot of the acoutc eergy projected the major lobe, whch the drecto perpedcular to the le ource. Fgure 9 how the correpodg preure cotour for cotuou le ource. Fgure 8 - reure at boudary by dtrbuted ource wth pacg 0.0m

11 Fgure 9 - reure cotour for dtrbuted ource wth pacg of 0.0 m Frequecy of 300 Hz ad 500 Hz have bee codered to exame the relatve error of ANSYS reult compared to aalytcal reult wth repect to the dtace of flow ource from the baffle. Fgure 0 how the relatve % error v. dtace of ource from the baffle. ercetage of error creae wth the cremet of dtace from the baffle, whch dered. However the relatve error decreae wth the creae of frequecy codered becaue the radu of crcular boudary larger. For example, Fgure ad Fgure how the preure at the radal boudary ad the preure cotour of the feld for dtace of ource of m from the baffle for hgh frequecy lke 000 Hz ad 3000 Hz. It ca be cocluded that ANSYS reult how good agreemet wth that of aalytcal reult whe flow ource placed away from baffle. Fgure 0 - Relatve error% v. dtace from the baffle for frequecy of 300 ad 500 Hz.

12 Fgure - reure at boudary for pot ource at a dtace of m from the baffle (f 000 Hz) Fgure - reure at boudary for pot ource at a dtace of m from the baffle (f 3000 Hz) Global reducto wth 0 pezo elemet ha bee mplemeted wth complex LMS method a a optmzato tool. A ANSYS macro fle, ADL (ANSYS parametrc deg laguage), ha bee ued to cotruct the trafer fucto matrx due to the actuator ad meauremet due to the oe ource oly both for oud level ad tructural dplacemet. Complex LMS method ha bee mplemeted th macro fle, whch wll gve the reducto of oud level, tructural vbrato db ad requred force the actuator wth all pezo elemet acto.

13 A frequecy of 0 Hz, whch cloe to modal frequecy of 8.4 Hz (coupled; tructure ad acoutc), ha bee codered to exame the global preure reducto ad tructural vbrato, alog the top of the elatc layer, ad reducto are foud to be 7.56 db ad 7.6 db repectvely. reure cotour, boudary preure ad tructural vbrato plottg, before ad after cotrol, for frequecy of 0 Hz have bee how Fgure 3 to 6. Fgure 3 - reure cotour for frequecy of 0 Hz (before cotrol)

14 Fgure 4 - reure cotour for frequecy of 0 Hz (after cotrol) Fgure 5 - reure alog the radal boudary for frequecy of 0 Hz (before ad after cotrol)

15 Fgure 6 - Dplacemet alog the top of the elatc layer for frequecy of 0 Hz (before ad after cotrol) Cocluo: Acoutc feld ad the tregth of ource ued ANSYS have bee decrbed ad the reult of varou cae aocated wth the acoutc preure feld creato ha bee compared wth the aalytcal reult. All reult are good agreemet wth the aalytcal outcome. h tudy provde a clear vew of the acoutc oe feld geerato the commercal fte elemet code, ANSYS. For -D acoutc FEM of ANSYS, the acoutc pot ource cyldrcal pot ource. he radu of crcular fte boudary crucal for the FEM reult. Actve cotrol of tructurally radated oud to a flud medum ha alo bee mplemeted ANSYS where pezo electrc materal ued a a cotrollg tool. he cot fucto that wa mmzed the um of the quared oud preure at the ode the flud medum. A mple cotrol ytem wth multple pezoelectrc actuator able to reduce the global oud level. It ca be cocluded that mmzato of oud feld radated by a ource for a gve exctato frequecy ca be acheved ug multple pezo elemet ANSYS. he actve cotrol tudy reported th paper prelmary whch lmted to the actve reducto of oud gle frequecy ad -D model wth mall umber of pezo elemet. 3-D model ad mult-frequecy oe reducto wth actve actuator ca be mulated for the future tudy. Referece: ) G. R. Lu, C. Ca, X. M. Zhag ad K. Y. Lam, Effect of ezocompote Coatg o Soud Radato ad Scatterg by a Submerged Cyldrcal Structure, 70 th hock ad brato Sympoum Nov. 5-9, 999, USA (Albuquerque, NM). ) ANSYS, Acoutc ad Flud-Structure Iteracto, A Revo 5.0 utoral, ANSYS, Ic., Jue 99. 3) ANSYS, "heory Referece, Releae 5.7," ANSYS, Ic., March. 00.

16 4). M. More ad K. U. Igard, heoretcal Acoutc, New York: McGraw-Hll, Ic., 968, pp ) Mguel C. Juger ad Davd Fet, Soud, Structure ad ther teracto, Cambrdge, Ma, MI pre, 97.