Sound Radiation of Circularly Oscillating Spherical and Cylindrical Shells. John Wang and Hongan Xu Volvo Group 4/30/2013
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1 Sound Radaton of Culaly Osllatng Spheal and Cylndal Shells John Wang and Hongan Xu Volvo Goup /0/0
2 Abstat Closed-fom expesson fo sound adaton of ulaly osllatng spheal shells s deved. Sound adaton of ulaly osllatng ylndal shells s also obtaned analytally fo low fequenes and fa feld. The expessons fo sound pessue, ntensty and powe ae deved. Sound pessue and sound powe level eduton s nvestgated. The eduton s quantfed. The theoy s ompaed wth test data. The applatons ae dsussed.
3 Bakgound Culaly osllatng moton of spheal shells an be deomposed as two pependula dpoles wth 90 degee phase shfts. Aousts dpole s well known A. D. Pee, Aousts, An Intoduton to Its Physs Pnples and Applatons. (Aoust Soety of Amea, 989) W. K. Blake, Mehans of Flow-Indued Sound and Vbaton. (Aadem Pess, In. 986) Dpole otatng about a pont away fom the dpole had been nvestgated Y. Mao, Y. Gu, D. Q, and H. Tang, An exat fequeny-doman soluton of the sound adated fom the otatng dpole pont soue. J. Aoust. So. Am. (), 9 0 (0). Rotatng Dpoles ae also studed n Quantum Mehans Ths study nvestgates the aousts dpole that otates about ts own ente o ulaly osllatng.
4 Physal Model Equaton of Moton Fgue My y ky ml e t y z x Soluton y( t) ml M n G( ) e ( t ) Cons. z x, z t M l m x, m z m If the suppots ae negleted ml ml x( t) sn t x ( t) ost M M ml ml z( t) ost z ( t) snt M M Two pependula dpoles wth phase dffeene / = A otatng dpole. O x A sphee wth eent mass onneted at the ente k
5 Rotatng Dpole Bounday Condton Geneal soluton Intodue funtons Bounday Condton M ml V t e V n V os os sn Re os sn os ˆ V V n a t a t x a t z os sn os e k Ak k os sn os ˆ e k Ak p k os sn os ˆ e k k Ak V k os sn os ˆ e k Ak V k os os sn ˆ ka e ka V a A ) (
6 Rotatng Dpole - Fa feld k Sound Pessue ˆ Ak pˆ Ak e k os sn os e os sn os k Sound Intensty ( ka) a I, av V os sn os ( ka) Sound Powe ˆ Ak V e k os sn os P av 0 I, av snd 0 d ( ka) ( ka) V a
7 Rotatng Dpole Fa feld and Low fequeny k ka Sound Pessue Sound Intensty ˆ Va k e k os sn os ( ka) a I, av V os sn os kva pˆ e k os sn os Sound Powe Vˆ k Va e k os sn os P av 0 I, av snd 0 d ( ka) V a
8 , Rotatng Dpole Deomposton p kv a os sn( t k) k p s kv a sn os os( t k) ka
9 Rotatng Dpole Sound Pessue p s p Two pependula dpoles wth 90 dg phase dffeene fom a otatng dpole p p p s
10 Rotatng Dpole Sound Intensty I av, I0 os sn os
11 Compae to Test Test Setup A fnte ylnde on abag and suppoted by fame though solatos. L=m, R=0.7m. Deep eessed end plates. The sufae of the ylnde was patally oveed. Eght dffeent eent speeds and mass settngs. =7.5m. Theoy The sound powe was alulated at the Eght test settngs. The adus was hosen to be 0.55m(Effetve Radus) due to ) A ylnde nstead of a sphee. ) Abag and ubbe mounts onneton. ) Patally oveed sufae.
12 dba Compae to Test 00 Sound Powe of Rotatng Dpole Theoy vs. Test Data Test Theoy a=0.55m Hz
13 Double Rotatng Dpole When b Fgue z We have, pˆ Ak s the phase dffeene k e os sn os e ˆ Ak V k e os sn os e O b x Va k p ( os) os sn( t k( a)) sn os os( t k( a) ( ka) ( ka) a I, av ( os) V os sn os ( ka) P av ( ka) V ( os) a ( ka) Sound s anelled f they ae out of phase
14 Double Rotatng Dpole Sound Pessue Va k p ( os) os sn( t k( a)) sn os os( t k( a) ( ka) / 8 / / 7 / 8
15 Double Rotatng Dpole Sound Intensty, os sn os ) ( ) ( ) os ( a V ka ka I av
16 Added/entaned mass Theoy: Low fequeny adaton fom sphees and ylndes p sphee V sphee k sn osw kr e R Vsphee a W V e t p ylnde kr e V k W ylnde sn os R V ylnde a L x R z R y O z O x L y
17 Summay Fomulaton of a sngle otatng dpole s developed. Numeal esults ae ompaed wth test data to show good oelaton. Double otatng dpoles ae fomulated and nvestgated to show potentals to edue the sound adaton. Low fequeny and fa feld solutons fo spheal and ylndal shells ae ompaed.
18 THANK YOU
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