Noise propagation simulation in and around buildings using improved integral energy equations

Transcription

1 ose oagato sulato a aou bulgs usg ove tegal eegy equatos Kyosh Masua Tase Cooato, Jaa ABTRACT If the alulato otos fo ose oagato a aou bulgs ae efetly sle, the age-soue etho o ay-tag etho a be ale. Howeve, otos ealty ae too olate to aly these ethos, beause the obato of ultle efletos a ffato ust be tae to aout. We have eveloe a extee tegal eegy equato etho to solve these obles. I the extee tegal eegy equatos, all eegy flows betwee the bouay eleets of a alulato oel ae obtae by solvg sultaeous equatos that tae ultle efletos, ultle ffatos a sou tassso to oseato. To ove the eso of the etho, the alulato of fst efletos s seaate fo the alulato of ultle efletos, a the fst efletos ae alulate by the aoxate etho eve fo the wave theoy. Ths etho s ale to the alulato of sous tastte though sall oegs. Petos usg ths etho oesoe well wth easueets fo atual sou fels. Keywos: ose oagato, tegal eegy equatos I-ICE Classfato of ubjets ube(s): 76.. ITRODUCTIO Whe esgg a bulg, t s otat to et the sou evoet a aou the bulg. A extee tegal eegy equato etho has bee eveloe fo ese etos of ose oagato a aou a ult-oo bulg suoue by othe bulgs. I ths etho, all eegy flows betwee bouay eleets of the alulato oel ae obtae by solvg equatos oseg ultle efletos, ultle ffatos a sou tassso. To ove the eso of ths etho, the alulato of fst efletos s seaate fo the alulato of ultle efletos, a the fst efletos ae alulate usg the aoxate etho eve fo wave theoy. Ths etho s ale to the alulato of sous tastte though sall oegs. Ths ae toues a theoy o ove extee tegal eegy equatos wth alulato exales.. CALCULATIO METHOD. Extee Itegal eegy Equatos I extee tegal eegy equatos, all eegy flows betwee the bouay eleets of a alulato oel ae obtae by solvg sultaeous equatos that tae ultle efletos, ultle ffatos a sou tassso to oseato. I the ogal tegal eegy equatos etho, the etvty of efleto s exesse as a lea obato of seula efleto a ao efleto as e Labet s law (). Hee, t s suose that oly ao efletos ae oat a seula efletos ae eglgble. Ths suosto saves eoy sae. I a sou fel suoue by bouay eleets as show Fgue, the et testy I j of the eleet oe j s gve by the followg tegal equato: Kyosh.asua@saua.tase.o.j Ite-ose 0 Page of 8

2 Page of 8 Ite-ose 0 I j WQ os s s Fgue Extee tegal eegy equatos os os I( Lff l QD l os l os os I( Whee W s the sou owe, Q s the etvty ex, s the total ube of eleets, s the aea of the eleet, a s the aea of eleet wth the sae shae o the ba of eleet. I( s the et testy at ot x a eleet a aoxate by testes of all oes the eleet usg teolato futo. s the sou absoto oeffet, s the sou tassso oeffet, s the agle of ee wth eset to the oal eto veto of the eleet otag the oe, s the stae betwee the oe j a ot x, s s the stae betwee the oe j a the sou soue, L ff s the ffato ath ube, a D l s the testy ue to ultle ffato at the oe j the ase whee a o-etoal sou soue s assue. By oseg the et testy of all oes, we a obta the tegal eegy equatos. The solutos of these equatos gve all et testes I a substtutg the solve I to Eq. (), the eegy esty E(x ) at ay ot the sou fel a be obtae. () Fgue Eegy esty alulato at eevg ots E( x ) WQ s os I( L ff l QDl M ff j D, j os os I( () Whee s the sou see, s the agle of aato eto wth eset to the oal eto veto of the eleet, s the stae betwee the ot x a the eevg ot, M ff s the ffato ath ube fo eleet to the eevg ot, a D,j s the testy ue to ultle ffato at the eevg ot the ase whee t s assue to be a o-etoal sou soue o the eleet. s s the stae betwee the sou soue a the eevg ot, L ff s the ffato ath ube fo the sou soue to the eevg ot, a D l s the testy ue to ultle ffatos fo the sou soue at the eevg ot. The alulato Page of 8 Ite-ose 0

3 Ite-ose 0 Page of 8 etho of the ffato testes D l a D, s esbe Ref. (). The alulato fequey s fo the 6 Hz to Hz otave ba.. Ioveet of Fst Refleto Calulato If thee ae few efleto sufaes the sou fel, the alulato eo eases beause Eq. () oes t ose seula efletos. To allevate ths oble, we eveloe a ew etho whh seaates the fst efleto alulato fo the efleto alulato tes Eq. (). The ew tegal equato fo the et testy exlug et sou testy I j of the eleet oe j s gve by Eq. (). I j M ef WQR os Fgue Iove tegal eegy equatos os os I ( Lff l l QD os l WQ os s os os I ( s The th te s the fst efleto alulato stea of a et sou alulato Eq. (). Hee, R s the fst efleto testy tasfe oeffet of the th efleto lae alulate by Eq. (), s the absoto oeffet of the th efleto sufae, a M ef s the total ube of efleto laes. The seo te alulates the sou tassso of eleet aato sou a the et sou fo the soue. R s alulate by Eq. (). os os R.9 (). 0 os f os The fouth equato Eq. () s use whe the le fo the agay soue ot to the oe ot osses the efleto sufae as show Fgue. I Eq. (), ± assues a egatve value whe s lage tha 90 egees. s the sufae aea of the efleto lae, f s fequey, a s wavelegth. These foulae wee eve fo aaet stuy usg Helholtz-Khhoff s equato. Fgue 5 shows the efleto sou essue level stbuto alulate usg Labet s law a Eq. (). The eso of the efleto sufae s ete by ete, a the sou absoto oeffet s zeo. The alulato fo the 6 Hz otave ba s vey sla to the ao efleto followg Labet s law. The efleto haatests beoe oe sla to those of seula efleto wth easg fequey. () Ite-ose 0 Page of 8

4 Page of 8 Ite-ose 0 Fgue Calulato of fst efleto sou Fgue 5 ou essue level stbutos alulate usg Labet s law a Eq. (). Ioveet of Tassso though all Oeg If thee ae sall oegs the sou fel, the alulato eo eases beause Eq. () oes t ose the tassso loss of sall oegs. To allevate ths oble, the alulato etho fo the fst efleto was ale to the alulato of sou tastte though sall oegs. A ew tegal equato that taes to aout tassso though sall oegs fo the et testy exlug et sou testy I j of the eleet oe j s gve by Eq. (5). I j M ef WQR os os I( Lff ts os QDl osl l WQ os s os os I ( s Whee T s the sall oeg tassso testy tasfe oeffet of the th sall oeg alulate by Eq. (6), a ts s the total ube of sall oegs. WQT os (5) Page of 8 Ite-ose 0

5 Ite-ose 0 Page 5 of 8 Ite-ose 0 Page 5 of 8 Fgue 6 Calulato of sall oeg tassso sou os 0 os 0 os os f T (6) The fouth equato Eq. (6) s use whe the le fo the soue ot to the oe ot osses the sall oegs as show Fgue 6. I Eq. (6), ± assues a egatve value whe s lage tha 90 egees. By oseg the et testy of all oes, we a obta the ove tegal eegy equatos. olvg these equatos gves all et testes I, a by substtutg the solve I to Eq. (7), the eegy esty E(x ) at ay ot the sou fel a be obtae. Fgue 7 Eegy esty alulato at eevg ots usg the ove etho ts ff ef ts ff s s s M M WQT QD WQR WQ T I D I E,, os os ) ( os os ) ( ) ( x x x (7) Whee M ts s the tassso ath ube fo eleet to the eevg ot though sall oegs, a T, s the testy ue to tassso though a sall oeg at the eevg ot the ase whee t s assue to be a o-etoal sou soue o the eleet. ef, ff, ts ae the ath ubes fo the sou soue to the eevg ot, a R, D, T t ae the efleto, ffato, a tassso testy tasfe oeffets.

6 Page 6 of 8 Ite-ose 0. EXPERIMET. Iove Calulato of Fst Refleto I oe to of the auay of the ew fst efleto alulato etho, a ose oagato exeet was oute a atual sou fel, as show Fgue 8. A -D alulato oel s show Fgue 8. Fgue 8 Exeet fo ove alulato of fst efleto The sou soue was a oeaheo seae whh aate ao boaba ose. The eevg ots wee set evey two etes the easueet aea show Fgue 8 a the ose levels wee easue. The owe level of the sou soue was estate by the sou essue levels at easueet ots ea the sou soue. The easue a alulate elatve ose level stbutos ae show Fgue 9. The alulato usg the ol etho whh alulates oly ao efletos ((b) Fgue 9) eostate goo oelato wth the atual easueets, but the alulato usg the ew etho, whh seaates off the fst efleto alulato (() Fgue 9), eostate bette oelato easueet aeas futhe fo the soue ot. Fgue 9 Exeetal esults fo ove alulato of fst efleto Page 6 of 8 Ite-ose 0

7 Ite-ose 0 Page 7 of 8. Iove Calulato of Tassso though all Oeg I oe to of the auay of the ew sall oegs tassso etho, a ose oagato exeet was oute a atual sou fel, as show Fgue 0. A -D alulato oel s show Fgue 0. Fgue 0 Exeet fo ove alulato of tassso though a sall oeg The sou soue was a oeaheo seae whh aate ao boaba ose the soue oo wth a bulg. The ao ose was tastte though the sall oeg a the oute glass wall, a oagate aou the bulgs. The eevg ots wee set evey two etes the easueet aea show Fgue 0, a the ose levels wee easue. The easue a alulate elatve ose level stbutos ae show Fgue. I the ol etho alulato, the sall oeg s set as a wall whose tassso loss s 0 B. The alulato usg the ol etho s to 6 B hghe tha the atual easueet ((b) Fgue ), but the alulato usg the ew etho, whh oses tassso though the sall oeg (() Fgue ), eostates bette oelato wth the atual easueet. Fgue Exeetal esults fo ove alulato of tassso though a sall oeg Ite-ose 0 Page 7 of 8

8 Page 8 of 8 Ite-ose 0. COCLUIO To ove the eso of the extee tegal eegy equatos etho, the alulato of fst efletos s seaate fo the alulato of ultle efletos, wth the fst efletos beg alulate usg the aoxate etho eve fo wave theoy. Ths etho was ale to the alulato of sou tastte though sall oegs. Petos usg ths etho oesoe bette wth the easueets fo atual sou fels tha the foe etho. REFERECE. Kuttuff H, ulete ahshalluve Rehteaeue t ffuse hallfel, Austa, 5, 97, -.. Masua K, ou evoet sulato syste fo eto of ose oagato a aou bulgs, AVA97 oeegs, 997, Page 8 of 8 Ite-ose 0