Dynamical Measurement of the Effective Radiation Area S D

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1 ynml Mesuement of the Effetve Rton Ae Wolfgng Klel 1 n Johm hlehte 1 Unvesty of Tehnology esen, Gemny, wklel@klele KLIPPEL GmbH, esen, Gemny, shlehte@klele Abstt The effetve ton e s one of the most motnt louseke metes beuse t etemnes the oustl outut (PL, soun owe) n effeny of the tnsue Ths mete s usully eve fom the geometl sze of the to onseng the mete of hlf the suoun e Ths onventonl tehnque fls fo mosekes n hehone tnsues whee the suoun geomety s moe omlte n the euson oes not vy lnely vesus us The e susses new methos fo mesung the moe esely The fst metho uses lse senso n mohone to mesue the voe slement n the soun essue genete by the tnsue whle mounte n sele enlosue The seon metho uses only the mehnl vbton n geomety of the to mesue by usng lse tngulton snne The e heks the elblty n eoublty of onventonl n the new methos n susses the ogton of the mesuement eo on the T/ metes usng test etubton tehnque n othe eve metes (senstvty) 1 INTROUCTION Eleto-oustl tnsues n be moele t low fequenes by n equvlent ut omsng few lume metes The effetve ton e esbes the oulng between the mehnl n the oustl omn by elng the one, hgm, suoun n othe tng ts by g ston movng wth the sme veloty s the voe n hvng n equvlent sufe genetng the sme soun essue n the f fel s the el to [1] The mete etemnes the soun essue on s (eg ss bn senstvty) n the totl oustl outut owe [] A ese vlue of s lso eequste fo ute mete mesuements usng the test etubton tehnque n fo ovng elble T/ metes (eg equvlent volume of ve stffness V s ) fo system esgn [3], [4] one ust suoun o fme In te the effetve ton e s usully eve fom the geomety of the tng sufe by eng the mete n the mle of the suoun e s shown n Fg 1 Fg 1: Estmtng the effetve ton e fom the to s geomety Ths oh onses the one movng s g boy n ssumes lne ey of the slement 1 (, ) o ( ) o fo fo / / / (1)

Klel, hlehte Effetve Rton Ae vesus us n the suoun e R mll showe n the en of [5] tht the mete efee to the hlf wth of the suoun s useful omton of 4 4 o 4 o 3 () s long s the suoun s not we thn 1 % of

2 Klel, hlehte Effetve Rton Ae vesus us n the suoun e R mll showe n the en of [5] tht the mete efee to the hlf wth of the suoun s useful omton of 4 4 o 4 o 3 () s long s the suoun s not we thn 1 % of the oute mete n the ssumton n Eq (1) s vl gnfnt hghe eos e foun n woofes usng lge suoun esgne fo elzng hgh ek slement X m n eselly n tweetes, hehones, hon omesson ves n mosekes whee the oute t of the hgm tself s use s susenson system Fg : Nonlne stbuton of one slement fo hehone ve In those ses the slement ses fom zeo t the oute m to the mml vlue t the voe oston by funton whh s usully nonlne (see Fg bove n Fg 8 n [5] n eens on the tul lmng onton of the m, the thkness n the uvtue of the hgm ofle n the mtel oetes Theoetl estmtons of effetve ton e fo lme ltes, flt ul membnes n othe smle geometes e gven n [6] but my be not lble to el tnsues hvng muh moe omlte geomety Thus the ese mesuement of the effetve ton e hs to be lulte fom the totl volume veloty q () mesue by usng mehnl n/o oustl sensos [7]-[9] The e oes wth ths oblem n sehes fo smle, obust n onvenent mesuement tehnques gvng moe elble vlues of At the begnnng the effetve ton e wll be efne by usng the soun essue outut ete by the Rylegh equton In the seon t the o n ons of the ttonl tehnques e susse A new tehnque s esente whh lultes the fom the vbton n to s geomety usng the esults of moen lse snnng tehnques The uy of the new metho s nvestgte n ome wth ttonl methos YMBOL (, obsevng ont n the f fel ont on the to s sufe stne between ente of the to n obsevng ont ngul fequeny ngul esonne fequeny ) omle soun essue t obsevng ont n the f fel () omle soun essue n the sele test enlosue (, ) omle slement t the to s sufe () omle voe slement () omle vlue of the effetve ton e eenng on fequeny effetve ton e esbng the ston moe t esonne ensty of totl to s sufe k wve numbe vg vegng us (usully t voe oston) oute us of the to q() totl volume veloty genete by the to C oustl omlne of the b volume n the sele enlosue V vton of the volume n the test enlosue V totl volume of the test enlosue stt essue bt ne V ( ) voe slement t esonne fequeny mesue n the wth enlge volume Pge of 9

3 Klel, hlehte Effetve Rton Ae o V ( ) soun essue t esonne fequeny mesue n the wth enlge volume nne mete of the suoun e oute mete of the suoun e mete efee to the mle of the suoun e q( ) j (, ) C emtte by ont soue n the ente of the to An equvlent volume veloty (6) q( ) j ( ) ( ) (7) bffle to - obsevng ont Fg 3: oun essue genete on s t obsevng ont by to mounte n n nfnte bffle 3 EFINITION OF A to mounte n bffle genetes soun essue jk (3) e, ) (, ) C t lstenng ont n the f fel usng the Rylegh Integl of omle slement (, ) ove ll onts on the sufe of the to s llustte n Fg 3 If the lstenng ont s on s, f wy fom the to n muh lge thn the mete of the to then the stne my be ssume s onstnt n Eq (3) smlfes to jk e, ) (, ) The sme soun essue, ) C j e q( ) jk (4) (5) n be genete by ston vbtng wth the efeene slement () n n effetve ton e () Combnng Eqs (6) n (7) gves the effetve ton e ( ) q( ) j ( ) (, ) ( ) whh s omle quntty n eens on fequeny (8) At low fequenes whee ll ts of the to vbte n hse the omle funton () beomes el vlue n the effetve ton e n be efne s ( ) (9) usng the funmentl esonne fequeny s useful efeene 4 MEAUREMENT TECHNIQUE The followng ynm mesuement tehnques mke no ssumton on the slement (, ) on the to s sufe 41 F-fel Mesuement n Bffle Usng Eqs (5) n (7) gves the fequeny eenent funton ( ) e jk, ) ( ) (1) s genete by volume veloty whh beomes the effetve ton e Pge 3 of 9

Klel, hlehte Effetve Rton Ae ( ), ) ( ) (11) ele volume t the esonne fequeny ong to Eq (9) Ths mesuement tehnque eques lbte mohone fo mesung the soun essue, ) on s t stne fom the to mounte n bffle

4 Klel, hlehte Effetve Rton Ae ( ), ) ( ) (11) ele volume t the esonne fequeny ong to Eq (9) Ths mesuement tehnque eques lbte mohone fo mesung the soun essue, ) on s t stne fom the to mounte n bffle The voe slement s mesue t multle onts on the sufe n vege to omenste fo non l-symmetl vbton moes Ths tehnque eques suffently lge bffle n n neho envonment t low fequenes Lse Mohone 4 Ne-fel Mesuement n Bffle Moeno et l suggeste n [5] mesuement of the soun essue, ) lose to the sufe of the to to el the equements ut on the oustl envonment n lultes the by, ) ( ) 4 ( ) (1) Howeve, Moeno [5] obseve sgnfnt nfluene of the to s geomety n mesue ffeene of moe thn 1 % n the vlue fo flt n onl stons of the sme sze 43 Bo Metho A to mounte on smll enlosue s shown n Fg 4 genetes soun essue ( ) q( ) jc b (13) whh s t low fequenes lmost neenent of the mohone oston [9] Fg 4: Mesuement of ntenl essue genete n sele enlosue Clultng the oustl omlne of the enlose C b V (14) by usng the volume V, the bt ne κ n the stt essue gves equvlent ton e V ( ) ( ) ( ) (15) The volume V of the n the test enlosue hs to be mesue efully onseng the fee volume of the enlosue n the sle by the louseke ts In te the etemnton of V lmts the uy of the mesuement tehnque 44 ffeentl Bo Metho Pefomng two mesuements wth ffeent volumes s llustte n Fg 5 senses wth the mesuement of stt volume sle by the tnsues slement () V () Pge 4 of 9

Klel, hlehte Effetve Rton Ae slement V () V () volume V Although the ffeentl uts the lowest equement on the oustl

Pefomng two mesuements whle usng two test enlosues whh hve ese ffeene n the volume V A ffeent oh fo etemnng n be

() Combnng Eq (15) of the fst mesuement wth V V V ( ) ( ) V (16) The slement n be mesue by tngulton lse wth vey

substtutng V n both equtons gves 1 V V V ( ) ( ) (17) ( ) ( ) z senso tnsue φ Fg 7: Lse snnng tehnque fo mesung

element suounng t, Fg 6: Pefomng ffeentl mesuement of the effetve ton e of hehone by usng synge A mel njeton um s

5 Klel, hlehte Effetve Rton Ae slement V () V () volume V Although the ffeentl uts the lowest equement on the oustl envonment the mjo svntge of ths tehnque s tht mno lekge my use sgnfnt eo n the mesuement 45 Lse Tehnque V V Fg 5: Pefomng two mesuements whle usng two test enlosues whh hve ese ffeene n the volume V A ffeent oh fo etemnng n be bse on the eltons shown n equtons (8) n (9) Thee s efne s the ntegte slement of the to sufe ve by the voe euson () Combnng Eq (15) of the fst mesuement wth V V V ( ) ( ) V (16) The slement n be mesue by tngulton lse wth vey hgh uy An utomt snnng tool n be use to mesue the slement, ) t mny onts on the to sufe (, of the seon mesuement n substtutng V n both equtons gves 1 V V V ( ) ( ) (17) ( ) ( ) z senso tnsue φ Fg 7: Lse snnng tehnque fo mesung vbton n geomety of the to s sufe The sufe ntegton s one by multlyng the slement t eh ont wth the esetve sufe element suounng t, Fg 6: Pefomng ffeentl mesuement of the effetve ton e of hehone by usng synge A mel njeton um s shown n Fg 6 my be use s n test enlosue fo mosekes, hehones n tweetes whh llows ese vton of the (,, ) ( ) ( ), (18) Pge 5 of 9

Klel, hlehte Effetve Rton Ae 451 Fequeny eeneny of () By lyng Eq (18) fequeny eenent effetve ton e () s obtne At low fequenes below the bek-u of the one the mltue of () s onstnt n eesents the effetve

6 Klel, hlehte Effetve Rton Ae 451 Fequeny eeneny of () By lyng Eq (18) fequeny eenent effetve ton e () s obtne At low fequenes below the bek-u of the one the mltue of () s onstnt n eesents the effetve ton e of the ston moton whh s equl to the T/ mete, ome Eq (9) Fg 8: Cone sufe elements, Fo the mesuement of the euson () t s vsble to mesue not only one sngle ont but the onut stl vegng by mesung multle onts eg on le lose to the voe ( ) (, vg, ) (19) The vegng us vg shoul be selete lose to the voe to be eesenttve fo the moton n ston moe Fg 1: Effetve ton e () vesus fequeny usng 8 ffeent vlues of fo vegng vg the voe slement The ghs of () e shown n Fg 1 fo set of ffeent n the ente of n ovl moseke vg Ove bo fequeny nge fom 1Hz to 1kHz the eve s nely onstnt An vegng n tht fequeny nge wll futhe move the uy of the nomnl of the ve vg At hghe fequenes () s not onstnt nymoe but eens on the sef vbton oetes t the vegng us vg n elton to the totl volume flow q () Fg 9: Use ntefe of the lulton tool eque to sefy the voe oston As long s the use vg s lose to the voe of the ve, the esetve () eesents lne tnsfe funton between gven slement () n the f-fel soun essue on s fo, see Eq () whh n be eve fom Eq (1) jk e (), ) ( ) ( ) Pge 6 of 9

Klel, hlehte Effetve Rton Ae 45 Avegng Rus vg Fg 1: Intensty lot of the one vbton (to) n setonl vew (bottom) of ul n ovl moseke An

the to wth enhne ek n bottom slement (to), slement vesus us (mle) n effetve ton e vesus t 1Hz vg In both ses full etle sn of 31 onts ws

fom the voe then the vg euson () wll obtn n eo whh les to n noet The mesue ghs fo n e shown n Fg 11 eenng on the loton of the vegng us

untl the oute ve ege Lkewse the eve s vl u to us of 7mm 453 Mesuement g esoluton The esoluton of the snnng g fo mesung the slement (,,

7 Klel, hlehte Effetve Rton Ae 45 Avegng Rus vg Fg 1: Intensty lot of the one vbton (to) n setonl vew (bottom) of ul n ovl moseke An nvestgton of the effet of eung the numbe of l n ngul mesuement onts ws onute fo the two mosekes shown n Fg 1 Fg 11: Coss setonl vew of the to wth enhne ek n bottom slement (to), slement vesus us (mle) n effetve ton e vesus t 1Hz vg In both ses full etle sn of 31 onts ws osene by emovng the t fom sngle mesuement o ngles The vegng us hs been set to 6mm fo the ul seke n to 1mm fo the ovl seke If s too f wy fom the voe then the vg euson () wll obtn n eo whh les to n noet The mesue ghs fo n e shown n Fg 11 eenng on the loton of the vegng us n fo fequeny of 1Hz It n be seen tht vg the mltue of the slement s nely onstnt n the ente of the ve u to us of 7mm n then t os to zeo untl the oute ve ege Lkewse the eve s vl u to us of 7mm 453 Mesuement g esoluton The esoluton of the snnng g fo mesung the slement (,, ) s motnt fo the uy of the etemne Fg 13: Clulte vlues of effetve ton e vesus l g esoluton (to) n ngul esoluton (bottom) fo ul seke Pge 7 of 9

Klel, hlehte Effetve Rton Ae ntegte sufe slement wll be too low whh les to n whh s lso too low Futhemoe the tngulton lse n oue eos whle mesung the vbton t sh eges o ooly efletve sots on the one These

8 Klel, hlehte Effetve Rton Ae ntegte sufe slement wll be too low whh les to n whh s lso too low Futhemoe the tngulton lse n oue eos whle mesung the vbton t sh eges o ooly efletve sots on the one These eoneous mesuement onts wll lso ffet the lulton of The snnng softwe use fo the esent emles n eognze eoneous onts by oeltng two subsequent mesuements fom ffeent stnes These onts wll be emove fom ny futhe nlyss by settng the mesue slement to zeo Agn the ntegte sufe slement wll be lowe eenng on the numbe n loton of the eoneous onts 5 ICUION Fg 14: Clulte vlues of effetve ton e vesus l g esoluton (to) n ngul esoluton (bottom) fo ovl seke The nomnl vlue fo emns vey ute fo the ul seke, even when only thee l lnes o lkewse fou ngul lnes wee ket Even ombnton of thee l n fou ngul stes wll esult n 3,375m² whh s only 1% wy fom the full esoluton esult of 3,48m² The lse tehnque oose n seton 45 efoms vbton mesuement of the omlete one Mesung the slement t sevel onts nste of only one ont s lso vsble fo the sngle tehnque n seton 43 n the ffeentl tehnque n seton 44 The eson s tht eselly smll sekes wth no oely enteng susenson e susetble to symmetl vbtons n okng moes s shown n Fg 15 Tht mens n ths se wth the mesue (,, ) t only 9 onts t s ossble to etemne the of the ve wth etble uy But t shoul be stte tht ths esult n not be le to ll ul sekes In genel t lest hghe l esoluton s neessy to ove oely the ey of the slement mltue tows lge As long s the ve she s s-symmetl, hghe ngul esoluton wll only move the sgnl to nose to of the mesuement n n hel to evlute the nfluene of okng moes oetly Fo the ovl seke the eo beomes lge f too few l o ngul stes e onsee Eselly hghe ngul esoluton s hee neessy to mesue the slement stbuton on n symmetl seke wth suffent uy The mesue one slement t shoul ove the omlete ve e to gve oe vlue fo by lyng Eq (18) But sometmes tht s not ossble eg when etn one egons e not essble by the lse beuse they e hen behn ove Then the Fg 15: Iegul one vbton These vbton moes usully ou t low fequenes whee the seke s suose to efom ston moton The slement mesue t only one ont wll not be eesenttve fo the moton of the omlete one n esene of symmetl vbton moes Pge 8 of 9

9 Klel, hlehte Effetve Rton Ae Theefoe t s neessy to efom set of vbton mesuements t selete onts on the one n vege the mesue t 6 CONCLUION An ute mesuement of the effetve ton e s the bss fo elble eton of the oustl outut An eo of 1 % n my use n eo of 1 B n ss bn senstvty Elotng the geomety of the to only by eng the mete n the mle of the suoun s the most smle tehnque whh my be lble to woofes whee the wth of the suoun s smll ome to totl mete of the to n the totl volume veloty s genete by the one vbtng s g boy Ths tehnque s not elble fo hehones, mosekes, omesson ves n othe tnsues whee the vbton ves sgnfntly vesus the to s sufe Hee the totl volume veloty hs to be mesue usng oustl n/o otl sensos The f fel mesuement suggeste n the e s smle tehnque gvng moe ute esults thn the ne fel mesuement but eques lge bffle n n neho envonment The ffeentl tehnque uts lowe equements on the test equment but eques eful selng of the test enlosue The mesuement of the voe slement eques mehnl mesuement whh n be omlshe by otl lse tngulton sensos The mesuement of multle onts s eque to onse non l-symmetl moes s foun on most tnsues sensng wth se If the to s sufe s omletely essble to n otl lse snne no oustl mesuements e eque n most ese vlue of the effetve ton e n be lulte fom the mesue vbton n geomety [3] Clk, Peson Mesuement of Louseke Pmetes, J Auo Eng oety 45, No (1997 Mh) [4] W Klel, U eel, Fst n Aute Mesuement of Lne Tnsue Pmetes esente t the 11 Conventon of the Auo Engneeng oety, 1 My, Amstem [5] J N Moeno, R A Mososo, Johnsson, Mesuement of the Effetve Rtng ufe Ae of Louseke Usng Lse Veloty Tnsue n Mohone" esente t the 96th Conventon of the Auo Engneeng oety, 1994 Febuy, Amstem, ent 3861 [6] R Blls, G Pfefe, R Wethshützky, Eletomehnshe ysteme e Mkotehnk un Mehtonk, nge Velg Beln Heelbeg 9 [7] J N Moeno, Johnsson, Hennng Bog Mesuement of Close Bo Louseke ystem Pmetes usng lse Veloty Tnsue n n Auo Anlyze, esente t the 9n Conventon of the Auo Engneeng oety, 199 Mh, Pent 335 [8] J N Moeno, Mesuement of Louseke Pmetes Usng Lse Veloty Tnsue n Two Chnnel FFT Anlyss, J Auo Eng o, Vol 39 (1991 Al) [9] K Anthony n J Ellot, A Comson of thee Methos of Mesung the Volume Veloty of n Aoust oue, J Auo Eng o, Vol 39, (1991 My) 7 REFERENCE [1] Leo Benek, Aousts, Aoustl oety of Ame, 31 [] R H mll, et-rto Louseke ystem Anlyss, J of Auo Eng o, Volume, (197 June) Pge 9 of 9

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