Sound Transmission Throough Lined, Composite Panel Structures: Transversely Isotropic Poro- Elastic Model
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1 Prde nvery Prde e-pb Pblcaon of he Ray. Herrc aboraore School of Mechancal Engneerng 8-5 Sond Tranmon Throogh ned, Comoe Panel Srcre: Tranverely Ioroc Poro- Elac Model J Sar Bolon Prde nvery, bolon@rde.ed Jeong-oo Km Follow h and addonal wor a: h://doc.lb.rde.ed/herrc Bolon, J Sar and Km, Jeong-oo, "Sond Tranmon Throogh ned, Comoe Panel Srcre: Tranverely Ioroc Poro-Elac Model" 5. Pblcaon of he Ray. Herrc aboraore. Paer 4. h://doc.lb.rde.ed/herrc/4 Th docmen ha been made avalable hrogh Prde e-pb, a ervce of he Prde nvery brare. Pleae conac eb@rde.ed for addonal nformaon.
2 Sond Tranmon Throgh ned, Comoe Panel Srcre: Tranverely e Ioroc o Poro-Elac o Model Prde nvery Jeong-oo Km J. Sar Bolon PRDE NIVERSITY
3 Bacgrond Convenonal rbbed-almnm felage Y X Honeycomb core Dfferen ffne n X,Y & Z dr. old and fld ar ar Relaced by Nome honeycomb andwch Panel Z Z Y Tranverely yoro-elac modelng Tranverely oroc roere 5 elac conan : E = E y, E,G,v y,v X Poro foam wh conan, oroy, bl deny, flow revy and oroy PRDE NIVERSITY
4 Movaon T erformance of honeycomb anel wore han hn almnm anel of ame ma/n area. Need o now ond ranmon characerc of he andwch anel Need o nderand he free wave roagaon characerc and o fnd concdence freqency. Predcon 5 Mearemen Almnm redcon T db Nome core Carbon hee K K FreqencyH PRDE NIVERSITY
5 Formlaon of Tranverely Ioroc Theory for ond ranmon lo model Sre-Sran Relaon -Tranverely y Ioroc Dynamc Relaon - wave eqaon Governng Dfferenal Eqaon Characerc Deron Eqaon Dlacemen feld - Harmonc wave -Z drecon Panel moon - Fleral wave - ongdnal wave Eernal rere -Incden + refleced rere P -Tranmed rere P ave roagaon olon Defne feld varable Tranmon coeffcen Bondary condon - Bonded anel - nbonded layer Average over ncdence angle Predcon of Sond Tranmon o PRDE NIVERSITY
6 Tranverely Ioroc Poro-elac Core. Sre - Sran Relaon y 3. Governng Dfferenal Eqaon R Qe M e G Q Ce Fe M Fe e A N Q F G G C M Ae A F G N G N e e M Q R Me M Q R Me Dynamc Relaon b q b q. Dynamc Relaon j e a j b 4. Harmonc dlacemen olon q b q b q j b e j e c j e d PRDE NIVERSITY
7 Tranverely Ioroc Model Characerc deron eqaon Sbon of harmonc olon no he governng eqaon lead o a e of homogeneo eqaon n mar form 4 6 j j e Ce Ce j j e Ce Ce 5 j j a b c d For here o be a nonrval olon, he deermnan of above eqaon m be ero A 6 4 A A3 A4 e e je je j 6 j j j 6 4 C e C e { { { { j j F Q F Q F Q F Q C Q } C e C Q } C e C Q } C e C Q } C e j j j j Three ar of wave nmber:, 3, 5 je j 4 { 6 5 F Q { F Q C Q } C e j C Q } C e j. PRDE NIVERSITY
8 3-layer andwch anel Sff anel + core + Sff anel Sff anel + core + Sff anel Feld varable Bondary condon a = j v a = j v 3 C C C h m D h m D TR C C C X 4 f n m D h j P 4 f r m D h j P c c R T TR TR TR S X f Tranmon Coeffcen PRDE NIVERSITY
9 Formlaon rocedre for Free wave n he andwch anel ave eqaon for Anoroc oro-elac core Remove fld colng erm Anoroc elac eqaon for core Characerc eqaon for anoroc oro-elac core Harmonc dlacemen olon Characerc eqaon for anoroc elac core Characerc eqaon for 3-layer andwch anel Symmerc & An-ymmerc form Combne anel moon - Fleral wave: - ongdnal wave: Solve nmercally Characerc eqaon for 3-layer andwch anel Symmerc & anymmerc form Ioroc and oen rface Raylegh-amb freqency eqaon Comle wave nmber for K and K Comle wave nmber for K and K PRDE NIVERSITY
10 Decomoon of dlacemen for core C co C co C co e ymm C n C n C n e an C C3 ymm n n 3 5C5n 5 e 3 C C 4 j an co co 3 5C 6co 5 e 3 j j j 3 ymm C co C3 co 3 5C5 co 5 e 3 3 an Cn C4n 3 5C6n 5 e 3 3 ymm C n C3n 3 5C5n 5 e 3 3 an Cco C4co 3 5C6co 5 e 3 here, C CC, C CC, C CC, ,, C C C C C C C C C j j j j PRDE NIVERSITY
11 Characerc eqaon of 3-layer andwch anel Smlfcaon a d, h Z 3 a d G h j Z f h Z h j Z f fll XG fll ll By eng he roere of he wo anel o be ame, and manlang he eqaon aroraely, he ymmerc and an-ymmerc form of he deron eqaon can be obaned. Decomoon Symmerc eqaon Eq. Eq.4 / Eq. Eq.5 / Eq.3 Eq.6 / G X ymm G ymm X Gymm C C C 3 5 An-ymmerc eqaon Eq. Eq.4 / Eq. Eq.5 / Eq.3 Eq.6 / T XGfll C C C C C C T GanXGan X Gan C C C 4 6 T PRDE NIVERSITY
12 Decomoon of wave nmber roo a H: Nome-honeycomb andwch anel 7 9 Symmerc comonen 8 An-ymmerc comonen PRDE NIVERSITY
13 Mode rajecore from H o H Nome-honeycomb andwch anel 6 Symmerc An-ymmerc 4 Re [m - ] Im [m - ] PRDE NIVERSITY
14 Mode rajecore from H o H A-foam-A andwch anel 6 Symmerc An-ymmerc 4 Re [m - ] Im [m - ] PRDE NIVERSITY
15 Mearemen of wave eed: A-foam-A andwch Mearemen Sm: fr ymmerc Predcon fr ymmerc [m - ] [m - ] FRF meared on boh face Freqency [H] Sb: fr an-ymmerc Freqency [H] fr an-ymmerc [m - ] [m - ] Freqency [H] Freqency [H] PRDE NIVERSITY
16 Analy of ST wh free wave eed: Honeycomb andwch 6 ymmerc #7 5 Predcon Mearemen 4 Phae Seed [m/ec] 4 an-ymmerc # T db 3 ma-law mode #5 3 Freqency [H] 3 Freqency [H] PRDE NIVERSITY
17 Analy of ST wh free wave eed: A-foam-A andwch 6 Predcon Mearemen nd ymmerc #7 5 Predcon Mearemen 4 Phae 4 Seed [m/ec] ymmerc #6 T db 3 ma-law an-ymmerc #3 Freqency [H] Freqency [H] PRDE NIVERSITY
18 Sffne conrol: hear modl G =.35 7 N/m G =.35 7 N/m G = N/m θ = 3º 6 5 Phae Seed m/ec 4 45º 7º Sonc lne by ncdence angle T 3 db 9º Freqency H Freqency H Eher ncreae or decreae of hear modl ncreae T PRDE NIVERSITY
19 Sffne conrol by hear modl of core: Sond ranmon lo a a arclar ncdence angle a θ = 3º b θ = 45º θ 6 T db 6 T db G =.35 7 N/m G =.35 7 N/m G = N/m Freq. H Freq. H c θ = 55º d θ =7º 6 6 T db T db Freq. H Freq. H PRDE NIVERSITY
20 Smmary of relaon beween Phae eed and ST Seronc ST ncreae a hae eed ncreae generally conrolled by he ffne Phae Seed m/ec Sonc lne a a arclar angle lowe ST ma addon very effecve Sbonc ST ncreae a hae eed deceae Conrolled by he ma law Freqency PRDE NIVERSITY
21 Conclon Tranverely oroc oro-elac model wa develoed for boh ond ranmon lo and free wave roagaon n he honeycomb andwch anel. The ymmerc and an-ymmerc free wave were nvegaed o denfy he concdence freqency and effec on he ond ranmon lo. The ond ranmon lo characerc were recely denfed by analyng he free wave roagaon along wh ncdence angle. The aramerc dy gge helfl gdelne for mrovng he ond barrer erformance of honeycomb andwch anel. PRDE NIVERSITY
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