Development of a noise reduction system with piezoelectric material to transmitted noise (Structure for improvement of the noise reduction effect)

Transcription

1 Dvlopmnt of a nois rduction systm with pizolctric matrial to transmittd nois (Structur for improvmnt of th nois rduction ffct) Katsuya YAMAMOTO 1 ; Akiyoshi ISHIMORI ; Hiroyuki SATO 3 ; Minyuki ASAHINA 4 Railway Tchnical Rsarch Institut, Japan ABSTRACT W prviously dvlopd a nois rduction systm consists of pizolctric matrial attachd on aluminum plat to rduc transmittd nois; th faturs and principls of this systm wr prsntd at th intrnois011. In that papr, ach aluminum plat with a pizolctric matrial (hrinaftr nois insulation panl: NIP ) was assumd to hav prfct flat plat and sam siz and thrfor has th idntical vibration charactristics. Howvr, whn panls wr bondd to a fram to form a singl structur, thir vibration charactristics actually diffrd, and th nois rduction capability of th systm bcam lowr. To solv this problm, w hav dvlopd a mthod in which planar tnsion is applid to ach NIP via a simpl fram structur. W hav vrifid that this mthod improvs th nois rduction and allows th targt frquncy to b tund. In this papr, w dscrib th faturs of this nw structur, and prsnt th rsults of our numrical analysis and xprimntal tsts. Kywords: Nois Rduction, Pizolctric matrial, Transmittd nois, Tnsion I-INCE Classification of Subjcts Numbr(s): INTRODUCTION Thr is dmand for a nw mthod for minimizing nois in our living and working nvironmnt; rducing low frquncy nois or vibration using lightwight matrials or quipmnt with pizolctric matrials prsnts a particular challng(1-7). W hav dvlopd a nw nois rduction systm that mploys an array of nois insulation panls (hrinaftr nois rduction systm ) to countract transmittd nois(8-10). This systm consists of a nois rduction unit an array of small flat panls to which pizolctric lmnts ar bondd and a control circuit in th form of an quivalnt inductanc circuit dsignd around oprational amplifirs. Th capacitanc of th pizolctric lmnts and th inductanc of th control circuit togthr form a rsonanc circuit, such that th nois passing through th nois insulation panls (NIPs) is rducd within a givn frquncy rang cntrd around th circuit s rsonant frquncy. This nois rduction systm was invstigatd undr conditions whr nois wavs incidnt to th NIPs wr planar, and all panls vibratd with th sam amplitud and phas. Undr ths conditions, whn all pizolctric lmnts on th panls ar connctd in sris or paralll, th transmittd nois is xpctd to b rducd by th control circuit. W vrifid xprimntally that th transmittd nois is rducd whn th lngth of th panl is shortr than th wavlngth of th incidnt nois in a lowr frquncy rang containing a fw hundrd frquncis. In addition, w stablishd that th optimum control conditions occur whn th (1,1) modal vibration frquncy of th NIPs and th rsonant frquncy of th lctrical circuit corrspond with th targt frquncy. This mans that th NIPs hav uniform vibration charactristics. Howvr, whn th NIPs ar adhsiv-bondd to a fram to construct a prototyp nois rduction unit (i.., a combination of an NIP and th fram), it is difficult to maintain consistnt vibration charactristics across multipl NIPs. Thrfor, it is mor ralistic to assum that th vibration 1 katsu@rtri.or.jp ishimori.akiyoshi.09@rtri.or.jp 3 sato.hiroyuki.06@rtri.or.jp 4 asahina@rtri.or.jp Intr-nois 014 Pag 1 of 10

2 Pag of 10 Intr-nois 014 charactristics of th NIPs ar not uniform, particularly in a handmad prototyp. Although control circuit inductanc can b asily adjustd using variabl rsistanc, it is much mor difficult to adjust th vibration charactristics of th panls onc thy ar fixd to th fram. This papr dscribs a prototyp structur in which th (1,1) modal vibration frquncy of th NIPs can b adjustd aftr bing attachd to a fram. Additionally, th abov ffcts and th improvd nois rduction charactristics obsrvd during acoustic xcitation tsting ar dtaild.. OUTLINE OF THE NOISE REDUCTION SYSTEM.1 Faturs and Principls of th Control (9) Th faturs of th nois rduction systm ar shown in Fig.1. Th systm consists of a control circuit and an array of NIP (mtal panls bondd to pizolctric matrials) and attachd to a fram. All pizolctric matrials in an NIP ar wird to ach othr in sris or paralll and connctd to th control circuit. This controllr is an quivalnt inductanc circuit basd on a simpl analog dsign using oprational amplifirs. Sinc pizolctric matrial is capacitiv, a rsonanc circuit is cratd btwn th pizolctric matrials and th control circuit. Th principl of control is as follows: whn th incidnt nois is input to th nois rduction unit, th NIPs ar xcitd at a frquncy rang cntrd around th rsonanc frquncy, and th pizolctric matrials gnrat a voltag. As th gnratd voltag is input to th control circuit, a voltag anti phas to th gnratd voltag rturns to th pizolctric matrials, causing an anti-phas forc to intract with th NIP. Th original vibration and th anti-phas forc cancl ach othr out, supprssing th vibration of th NIP. As th vibration is rducd, th nois transmittd through that panl also rducs. This vibration rduction ffct, which is producd whn an inductiv lmnt is connctd to a pizolctric lmnt, is rportd to b quivalnt to th ffcts of applying a mchanical dynamic vibration absorbr. Whn svral pizolctric matrials ar wird to th nois rduction unit, thy act as an quivalnt capacitanc and th vibration of all NIPs is rducd by th uniform anti-phas voltag input to th pizolctric matrials from th control circuit. Whn th nois rduction unit is installd on any targt panl, a layr of air is formd btwn th two. As th acoustic powr in th air layr is supprssd by th nois rduction systm, th nois transmittd through th targt plat is also rducd, rgardlss of its vibration charactristics. Figur 1(a) suggsts that th systm rducs only th transmittd nois whn th panl is placd on th Pizolctric matrial Fram Air layr NIP Transmittd nois Incidnt nois Mtal Plat Targt plat Control circuit Fram Nois rduction unit Nois insulation panl (NIP) (a) Nois rduction panl (b) Cross-sctional viw Fig.1 Outlin of th nois rduction systm Pag of 10 Intr-nois 014

3 m L s Θ m m Intr-nois 014 Pag 3 of 10 incidnt nois sid of th targt plat and structur bon nois whn th panl is installd on th transmittd nois sid. This nois rduction systm has svral advantags: (1) It is not ncssary to idntify th vibration charactristics of th targt panl or th sound charactristics of th transmittd nois. ()Hnc, this systm can rduc transmittd nois without rquiring snsors such as microphons or acclration pickups. (3)Sinc th controllr is composd of an oprational amplifir circuit and th pizolctric matrial is drivn according to th input voltag, powr consumption is low. (4)As th nois rduction panl and th control circuit can b mass producd, this systm can b ralizd inxpnsivly.. Modl of th Nois Rduction Systm (9) Svral studis hav dalt with nois rduction systms that us pizolctric matrial. Sinc our nois rduction systm implmnts control by conncting an lctrical circuit to pizolctric matrials, th whol systm contains both a mchanical subsystm (an NIP) and an lctrical subsystm (th pizolctric matrials and control circuit). In prvious rsarch, it was dmonstratd that ths systm can b convrtd to an quivalnt mchanical systm(11-1). Figur (a) shows th actual circuit formd whn all pizolctric matrials ar connctd in sris, and Fig. (b) is th quivalnt mchanical systm. Th inductanc, rsistanc Rs, and capacitanc C in th actual circuit of Fig. (a) can b convrtd to an quivalnt addd mass Ls, an quivalnt damping lmnt R, and an quivalnt stiffnss lmnt C, as shown in Fig. (b), using th lctromchanical coupling cofficint of th pizolctric matrial, whr p is th amplitud of th incidnt nois prssur, w is th displacmnt of an NIP, m is th modal mass, c is th modal damping cofficint, and k is th modal stiffnss of an NIP. In a prvious study, th vibration rduction ffct w of an NIP whn th capacitanc C of all pizolctric matrials is assumd to b th sam has alrady bn obtaind against th displacmnt w 0 without control, as shown blow. w GiR GiI Δ w= =, w G G G G 0 ir R ii I w 0, p m jc k () GiR L s GiI Pizolctric matrial q R s L s (a)actual modl Fig. A modl of th nois insulation panl with inductanc circuit C Nois insulation panl p w m, k, c R s Θ Θ /C Θ /C Θ /C ξ w (b)equivalnt mchanical modl N 1 1, (3) N,, (4) w w p c p k c p c k k (1) Intr-nois 014 Pag 3 of 10

4 TypA:310, TypB: Rduction ratio of th vibration lvl of th nois insulation panl (db) Pag 4 of 10 Intr-nois 014 G R G I ,, m m, (7), 1 (8), (9) s p m L : in sris, L : in paralll, (10) c, (11) m 1 R, (1) m whr j is th imaginary unit, is th angular frquncy, 1 is th (1,1) modal natural angular frquncy of an NIP, and is displacmnt of th quivalnt addd mass. Th quivalnt lctrical mass in Eq. (10) is slctd dpnding on whthr th pizolctric matrials ar connctd in sris or paralll. Th combind capacitanc Cs of th pizolctric lmnts is rlatd to inductanc Ls bcaus of th formation of a rsonanc circuit btwn th combind capacitanc Cs and inductanc Ls, whr s dnots th rsonant angular frquncy (hrinaftr lctric rsonanc frquncy). Th natural frquncy of (1,1) mod is sparatly drivd as follows(13): 1 m n D fmn. (13) a b h Microphon Transmittd nois Nois rduction panl or nois rduction unit Incidnt nois Spakr TypA:65, TypB:375 Fig.3 Exprimntal stup (TypA: Smallr Box, TypB: Largr Box) Fram Nois insulation panl Exprimntal Analytical (5) (6) Frquncy (Hz) Fig.4 Control ffct by four nois insulation panls (th pizolctric loudspakr) Incras Dcras Pizolctric matrial Fixd by adhsion bond Fig.5 Cross-sctional viw of th convntional structur of a nois insulation unit Pag 4 of 10 Intr-nois 014

5 FRF of th vibration lvl of NIP(dB) 10dB Th nois rduction ffct of ach NIP (db) Total Nois rduction ffct of th nois rduction panl (db) Intr-nois 014 Pag 5 of 10 Hr, a and b ar th lngth and bradth of a rctangular plat, is dnsity, D is flxural rigidity, and h is thicknss. On th basis of th abov thory, w hav confirmd th nois rduction capability of our dsign with a systm using a pizolctric loudspakr (Panasonic, WM-R57A:50*40mm) as an NIP. In this tst, th nois rduction array (or th nois rduction unit) was st on a box in which th loudspakr was installd, as shown in Fig. 3, and a microphon was usd to masur th transmittd nois. W vrifid that th vibration charactristics of th NIPs could b valuatd using th frquncy rspons function of th voltag gnratd by a pizolctric matrial, taking th sound prssur lvl in th box as th incidnt nois. In th frquncy rang cntrd at th natural frquncy of (1,1), valuation of vibration charactristics was largly basd on th transmittd nois. Figur 4 shows a comparison btwn th nois rduction capability of th xprimntal systm and th analysis basd on Eqs. (1) (1). Sinc th natural frquncy of (1,1) mod was about 160 Hz, th vibration was supprssd by mor than 30 db. This nois rduction systm is considrd quivalnt to a dynamic vibration absorbr. Thus, th nois in th sid bands incrasd in accordanc with that thory. Although this pizolctric loudspakr is ffctiv as an NIP, its vibration charactristics cannot b modifid. As a nxt stp, w trid to dvlop an NIP using an aluminum plat and pizolctric matrials to achiv nois rduction at arbitrary frquncis. This systm comprisd cramic pizolctric matrials attachd to aluminum plats adhsiv-bondd to an ABS fram. Figur 5 shows a cross-sctional viw of that unit. Transmittd nois cntrd at th natural frquncy of (1,1) mod of th NIP was rducd sufficintly. 3. PROBLEMS TO BE SOLVED For xpanding th nois rduction ara, w manufacturd a largr nois rduction panl composd of four NIPs, as shown in Fig. 6; its dimnsions ar providd in Tabl 1. This unit was mountd on a tst box, as shown in Fig. 3, and th vibration charactristics of th NIPs wr masurd. Th rsults ar shown in Fig. 7. Fig.6 A prvious nois rduction panl with four nois insulation panls Tabl 1 Dimnsions of a prvious nois rduction panl Siz of a NIP 100*100 mm Siz of a pizolctric matrial 50*50 mm Thicknss of an aluminum plat 0.3 mm Thicknss of a pizolctric matrial 0.3 mm Matrial of th fram ABS NIP1 NIP NIP3 NIP Frquncy (Hz) Fig.7 Vibration charactristic of th prvious NIP Incras Dcras NIP1 NIP3 Total NIP NIP Frquncy (Hz) Fig.8 Nois rduction ffct (Total: right axis) Incras Dcras Intr-nois 014 Pag 5 of 10

6 Pag 6 of 10 Intr-nois 014 It can b sn that th vibration paks of all NIPs appard btwn 0 and 70 Hz, so th vibration around this frquncy rang was dominatd by th (1,1) vibration mod. Howvr, th vibration charactristics wr not consistnt, suggsting that whn th NIPs ar fixd to a fram with th sam spcifications and procdur, thir vibration charactristics diffr. Undr ths conditions, th two pizolctric matrials wr connctd in sris, and two sts wr connctd in paralll. Finally, this st of pizolctric lmnts was connctd to th control circuit. By masuring th transmittd nois at a distanc of 300 mm from th nois rduction unit and vry clos to th NIP, w compard th frquncy rspons functions of th transmittd nois and th input nois with and without control. Th targt frquncy was 7.5 Hz, and th inductanc of th control circuit was tund to that frquncy. Th nois rduction ffcts ar shown in Fig. 8. Whil th nois transmittd through NIPs 1 and 4 wr rducd by mor than 5 db, nois rduction by panls and 3 was almost 3 db. W considr this diffrnc in nois rduction to b influncd by th vibration charactristics of th NIPs. In particular, whn an NIP has slack aras and is not flat, th control forc gnratd by th pizolctric matrial might not propagat across th ntir ara of th plat, such that th ffcts rquird in ordr for th plat to stiffn do not appar. Sinc such variations in NIP vibration ar considrd invitabl whn a thin NIP is fixd to th fram by adhsiv bonding, th importanc of crating uniform vibration charactristics is clar. 4. SOLUTIONS TO THE PROBLEM As discussd abov, in this nois rduction systm, it is important that NIPs vibrat th sam vibration charactristics to produc th nois rduction ffct sufficintly. Morovr, th targt frquncy and th natural frquncy of (1,1) mod must coincid. Othrwis, th nois will not b sufficintly rducd. Howvr, prsrving ths vibration charactristics whil fixing th NIPs to th fram is difficult, ncssitating a mans for adjusting th NIPs vibration charactristics aftr fixation. W propos a mthod for applying pr-tnsion to ach NIP as a countrmasur against th problm dscribd abov. Our mthod is basd on th following two ffcts. First, th vibration charactristics of th plat should improv if th NIP is fixd loosly to th fram according to th fixation procdur. Scond, th natural frquncy of (1,1) mod can b adjustd bcaus of th wll-known ffct of tnsion on vibration charactristics. Th rlationship btwn vibration and Fram tnsion in a rctangular plat is known to b NIP as follows. In a rctangular plat with all four dgs simply supportd, th natural frquncy of (1,1) mod with tnsion is givn Pizolctric as follows(14): matrials Squar bar Scrw Fig.9 A cross-sctional viw of th nw structur of a nois rduction panl Aluminum plat (150*150*t0.4mm) Squar bar Aluminum plat Forc Pull down forc Fram Pivot point Squar bar (a) Top-down viw (b) Bottom-up viw (c) Cross-sctional viw Fig.10 A numrical analysis modl of a NIP Pag 6 of 10 Intr-nois 014

7 Natural frquncy of (1,1) mod (Hz) Intr-nois 014 Pag 7 of 10 [MPa] (a) 0 N (b) 500 N pull (Initial condition) Fig.11 Rsult of th numrical analysis Pull down forc (N) Fig.1 Chang in th (1,1) modal vibration frquncy 1 1 m n m n fmn D N1 N. (14) h a b a b W dvisd a structur for asily applying pr-tnsion to an NIP. A cross-sctional viw of th NIP is shown in Fig. 9. Th NIP is attachd to a fram via four squar bars, which ar tiltd on th fram to b slightly angld, such that th angl of th bar and th pr-tnsion of th NIP can b adjustd through th tightning forc of th scrws. In addition, th amount of pr -tnsion can b controlld by adjusting th angl or torqu of th scrws. A numrical analysis was carrid out to invstigat pr-tnsion charactristics and changs in th natural frquncy of (1,1) mod in an NIP. Figur 10 shows a modl of th analysis. Th NIP was thin aluminum, th squar bars wr Baklit spcifically, and th fram was assumd to b a rigid body. In this analysis, pr-tnsion was applid to th NIP by a forc that pulls on sid of th squar bar down to th fram, instad of th tightning forc of th scrw. Figur 11 shows th strss xrtd on th NIP by th forc from th squar bar. W confirmd that whn th squar bar applis this forc, pr-tnsion is xrtd across th ntir ara of th NIP. Nxt, w calculatd th natural frquncy of (1,1) mod with th applid downward forc. Figur 1 shows th rlationship btwn th downward forc and th natural frquncy of (1,1) mod. Having vrifid that th natural frquncy of (1,1) mod incrass in proportion to th downward pulling forc, it appars that th natural frquncy of (1,1) mod can b adjustd by applying pr-tnsion to th NIP. 5. VERIFICATION OF THE TUNING METHOD OF NATURAL FREQUENCY OF THE NIP W manufacturd a prototyp NIP, shown in Fig. 13. Th nois rduction unit was mountd on th tst box, as shown in Fig. 3, and th rlationship btwn th natural frquncy of (1,1) mod of th NIP and th rotation angl of th scrw was valuatd. Th rsult is shown in Fig. 14. Hr, Initial rprsnts th condition that th had of a scrw shown in Fig.9 lightly touchd on th fram, i.. only a littl pr-tnsion was applid to th NIP. Th natural frquncy of (1,1) mod at th initial angl was 03Hz, as shown in Fig. 14. Th profil of th vibration charactristics changd to bcom chvron-shapd compard with th vibration charactristics in Fig. 7, and th pak bcam distinct. As a rason of th improvmnt to th vibration charactristic without applying pr-tnsion, th NIP might to b a nar-flat condition by bnding th aluminum Fig.13 Th nw typ nois rduction unit Intr-nois 014 Pag 7 of 10

8 Natural frquncy of (1,1) mod (Hz) FRF of th vibration lvl of NIP(dB) 10dB Pag 8 of 10 Intr-nois 014 Initial 90 Dgr 180 Dgr 70 Dgr 360 Dgr 450 Dgr 540 Dgr 630 Dgr 70 Dgr Frquncy( Hz) Fig.14 Chang of th vibration charactristics of a NIP Fastn Loos Th tigntning angl (dg) Fig.15 Th chang of th (1,1) modal vibration frquncy plat at th dg of th squar bar. Although th natural frquncy of (1,1) mod hardly changd btwn th initial angl and 90 of tightning, it did gradually incras as th scrw was tightnd, finally raching 48 Hz in two turns of tightning (70 of tightning), i.., it incrasd by around 50 Hz. Th rlationship btwn th scrw angl and th natural frquncy of (1,1) mod with tightning and loosning is shown in Fig. 15. Although hystrsis was apparnt in som rangs, th natural frquncy of (1,1) mod changd in proportion to th scrw angl, thus dmonstrating th fasibility of applying pr-tnsion to th NIP and adjusting th natural frquncy of (1,1) mod according to th tightning angl. 6. IMPROVEMENT OF THE NOISE REDUCTION PERFORMANCE BYTUNING THE NOISE REDUCTION PANELS In th prvious sction, it was vrifid that th natural frquncy of (1,1) mod could b adjustd by applying pr-tnsion to th NIP. To dmonstrat th application of this mthod, w manufacturd a nois rduction panl with four intntionally diffrntly sizd NIPs, and with th natural frquncy of (1,1) mod tunabl by mans of th tightning forc of th scrws on th bar. Nois rduction ffcts wr valuatd aftr conncting an inductanc circuit for control. Figur 16 shows th nois rduction unit, and Tabl shows its spcifications. Th vibration charactristics of th NIPs in th initial condition, with th scrws compltly unfastnd, ar shown in Fig. 17. Th pak frquncy appard at around 140 Hz for NIPs 1 and, and at around 160 Hz for NIPs 3 and 4. In thory, if th siz of an NIP is largr, th pak frquncy will b lowr, and vic vrsa. Howvr, th pak frquncis appard in two frquncy rangs du to subtl diffrncs in conditions. W tightnd th scrws of NIP 4 with a small amount of torqu and tund th natural frquncy of (1,1) mod to 170 Hz. Pr-tnsion was incrmntally applid to NIPs 1 to 3, and th (1,1) modal frquncis of all NIPs wr tund to 170 Hz, as shown in Fig. 18. Pag 8 of 10 Intr-nois 014

9 Nois rduction ffct of ach NIP (db) Total nois rduction ffct of th nois rduction panl (db) FRF of th vibration lvl of NIP(dB) 10dB FRF of th vibration lvl of NIP(dB) 10dB Intr-nois 014 Pag 9 of 10 Fig.16 Th nw typ nois rduction panl with four NIP Tabl Spcification of a nw nois rduction panl Siz of a NIP 1 Siz of a NIP Siz of a NIP 3 Siz of a NIP 4 Siz of a pizolctric matrial Thicknss of a aluminum plat Thicknss of a pizolctric matrial Matrial of th fram 150*150 mm 148*148 mm 146*146 mm 144*144 mm 63*63 mm 0.4 mm 0.4 mm Baklit NIP1 NIP NIP3 NIP4 NIP1 NIP NIP3 NIP Frquncy (Hz) Fig.17 Initial vibration charactristic of ach NIP Frquncy (Hz) Fig.18 Vibration charactristic of ach NIP aftr tuning Incras Dcras Frquncy (Hz) 80 NIP Fig.19 Nois rduction ffct of nw typ NIP (lft axis) and th nois rduction panl (right axis) Finally, four pizolctric matrials wr wird to ach othr (in a - sris paralll configuration) and connctd to an inductanc circuit. Th inductanc was tund to an lctrical rsonanc frquncy of 170 Hz, and th ffct upon nois transmission was masurd. Th rsult is shown in Fig. 19. Th transmittd nois was supprssd by mor than 0 db by ach NIP, with a total nois rduction of about 5 db. Th nois incrasd at Hz or Hz in agrmnt with th dynamic vibration absorbr thory. Th structur was thus dmonstratd to offr improvd nois rduction charactristics. NIP1 NIP3 Total NIP4 Incras Dcras Intr-nois 014 Pag 9 of 10

10 Pag 10 of 10 Intr-nois CONCLUSION W confirmd that th diffrnc of th natural frquncy of th NIP xrt influnc to th nois rduction prformanc, and proposd th structur to adjustabl th vibration charactristics of th NIP. 1. Whn an NIP is fixd to a fram with an adhsiv bond, it will almost invitably affct th vibration charactristics of th NIP, and it is impossibl to subsquntly tun thos charactristics.. Variation of natural frquncy of th (1,1) mod of th NIP causs prformanc dgradation of th nois rduction systm. 3. A nois rduction panl with thus altrd vibration charactristics cannot gratly rduc th transmittd nois. 4. By applying pr-tnsion to ach NIP, th vibration charactristics improv significantly 5. A structur that can asily apply pr-tnsion to th NIPs is prsntd. 6. Th vibration charactristics of th nois rduction unit corrspond with th diffrnt vibration charactristics of th NIPs, and significant improvmnts in transmittd nois ar dmonstratd. REFERENCES 1. Wu SY. Pizolctric shunts with a paralll R-L circuit for structural damping and vibration control. Proc SPIE 1996; 6 Jan- Fb 1996; San Digo, USA 1996.p Fin OM. A modl for pizo-rsistiv damping of two-dimnsional structurs, Journal of sound and vibration.008;310:p Flming AJ, Mohimani SO. Synthsis of optimal pizolctric shunt impdancs for structural vibration control. Proc SPIE 004; Mar 004; San Digo, USA 004. p Flming AJ, Bhrns S, Mohimani SO. An Autonomous Pizolctric Shunt Damping Systm, Proc SPIE 003; -6 Mar 003; San Digo, USA 003. p Kim SM, Wang S, Brnnan MJ. Dynamic analysis and optimal dsign of a passiv and an activ pizo-lctrical dynamic vibration absorbr, Journal of sound and vibration.011;330:p Casadi F, Dozio L, Ruzzn M, Cunfar KA. Priodic shuntd arrays for th control of nois radiation in an nclosur, Journal of sound and vibration.010;39:p Bin T, Elliott S, Frralli L, Caslla M, Mschk J, Samann E, Nilsn FK, Kropp W. Intgratd Solutions for Nois & Vibration Control in Vhicls. Procdia - Social and Bhavioral Scincs. 01; 48:p Yamamoto K, Asahina M, Mamada S, Sato D. Dvlopmnt of a Nois Rduction Systm with Pizolctric Matrial to Transmittd Nois (Fatur and Control Principl). INTER-NOISE 011; 4-7 Sptmbr 011; Osaka, Japan 011. CD-ROM. 9. Yamamoto K, Tanaka N, Asahina M. Dvlopmnt of a Systm to control nois transmittd through intrnal panls of railway vhicl (nd rport, Proposal for a Nois Control Systm Arrayd th Nois Insulation Panls). Transactions of th Japan Socity of Mchanical Enginrs, Sris C. 009; 75(75): p Yamamoto K, Asahina M, Mamada S, Sato D. Dvlopmnt of a Systm using Pizolctric Matrials to Rduc th Intrior Nois of a Railway Vhicl. Nois and Vibration Mitigation for Rail Trans. Sys., Springr 01:p Yamada K, Matsuhisa H, Utsuno H, Sawada K. Optimum tuning of sris and paralll LR circuits for passiv vibration supprssion using pizolctric lmnts., Journal of sound and vibration. 010; 39: p Yamada K, Matsuhisa H, Utsuno H, Park JG. Hybrid vibration supprssion of flxibl structurs using pizolctric lmnts and analog circuits. JSME Journal of Environmnt and Enginring 3 (). 008: p Fahy F. Sound and Structural Vibration. Acadmic prss. 1987:p Lissa A. Vibration of plats. Acoustical Socity of Amrica. 1973:p Pag 10 of 10 Intr-nois 014