THE STEADY-STATE VIBRATION RESPONSE OF A BAFFED PATE SIMPY-SUPPORTED ON A SIDES SUBJECTED TO RANDOM PRESSURE PANE WAVE EXCITATION AT OBIQUE INCIDENCE Revisi A By T Irvie Deceber 7, 04 Eil: @vibrid.c The rd ecii pper is very siilr Referece which cvered hric ecii. The bffled, siply-suppred ple i Figure is subjeced blique ple pressure wve e side. Oly side view lg he legh is shw becuse he pressure is ssued be uifr wih widh. This digr d he crrespdig pressure field equi re e fr Referece. Direci f Prpgi Wvefr Wvefr w(,y,) Figure. is he cusic wvelegh. is he rce wvelegh. / ()
The gverig differeil equi fr Referece is 4 4 4 w w w z D h P(, ) 4 4 y y () The ple siffess fcr D is give by where Eh 3 D (3) E H P is he dulus f elsiciy Piss s ri is he hicess is he ss desiy (ss/vlue) is he pplied pressure The ss-rlized de shpes re y b h b (4) y b h b (5) y b h b (6)
y y b h b b y y b h b b (7) (8) The url frequecies re c D h b (9) D h b (0) e b () Thus D h () c 4 D h (3) The geerlized frce is y b h b (4) e  (5) bh 3
4 b y  (6) b 0 0 ddy ) p(, b y  () (7) b 0 0 ddy b y  p () (8) b 0 0 ddy b y  p () (9) b 0 0 b y d  b p () (0) 0 d p  b () () 0 d p  b () () 0 0 d d p  b () (3)
Fr, () Â b p (4) Ne h fr ll vlues, 0 (5) () Â b p (6) Â b () p (7) () Â p b (8) 5
6 b  p () (9) b  p () (30) V (3) b  p () (3) The phse gle ε will be regrded s rbirry ce ly sedy-se slui is sugh. b  p () (33)
7 Ne he fllwig reliship fr he dl wvelegh. (34) (35) 4 b  p () (36) b  p () (37) b  p () (38) Fr rbirry phse gle, he equi y be rewrie s fr, b  p () (39)
Fr, Â p b () (40) Agi, ly he sedy-se slui is eeded. S defie pricipi fcr d represe he ie vryig er s hric ecii fuci. where () p() (4) p() p ep( j ) (4) Fr, Â b (43) Fr, Â b (44) 8
Defie ji ccepce fuci J. J  b (45) J (46)  b Fr, J (47) The equi f i fr he dl crdies is d u d du u p() (48) d d u d du u  J p() (49) d The eprl vrible respse he pplied frce rspsed he frequecy di is U P (50) j 9
 b J U P (5) j Recll (5) w(, y, ) (, y)u Trspse he frequecy di. (, y) W, y, P (53) j  b J (, y) W, y, P (54) j The frequecy respse fuci relig he displcee he blique pressure field is W, y, P (, y) j (55) W, y, P  J (, y) j (56) The bedig es re M, y, D W, y, y (57) 0
Myy, y, D W, y, y (58) The bedig sresses fr Referece 3 re Ezˆ y, y, W, y, (59) Ezˆ yy y, y, W, y, (60) Ezˆ y, y, W, y, y (6) ẑ is he disce fr he ceerlie i he vericl is A eple is give i Appedi B. Refereces. T. Irvie, The Sedy-Se Vibri Respse f Bffled Ple Siply-Suppred All Sides Subjeced Hric Pressure Wve Ecii Oblique Icidece, Revisi E, Vibrid, 04.. T. Irvie, The Me Squre Frce Due Rd Frces Rigid Be, Revisi B, Vibrid, 04. 3. J.S. R, Dyics f Ples, Nrs, New Delhi, 999. 4. T. Irvie, Sedy-Se Vibri Respse f Ple Siply-Suppred All Sides Subjeced Uifr Pressure, Revisi C, Vibrid, 04. 5. E. Richrds & D. Med, Nise d Acusic Figue i Aeruics, Wiley, New Yr, 968.
APPENDIX A Mgiude f Cple Trigeric Ter V (A-) V (A-) V (A-3) V (A-4) V (A-5) V 4 (A-6) V (A-7) 3
APPENDIX B Eple Csider recgulr ple wih he fllwig prperies: Budry Cdiis Meril Siply Suppred All Sides Aluiu Thicess h = 0.5 ich egh = 0 ich Widh b = 8 ich Elsic Mdulus E = 0E+06 lbf/i^ Mss per Vlue v = 0. lb / i^3 ( 0.00059 lbf sec^/i^4 ) Mss per Are = 0.05 lb / i^ (3.4E-05 lbf sec^/i^3 ) Viscus Dpig Ri = 0.03 fr ll des The rl des d frequecy respse fuci lysis re perfred vi Mlb scrip. 4
The rl des resuls re: Tble B-. Nurl Frequecy Resuls, Ple Siply-Suppred ll Sides f (Hz) 30 656 855 09 46 3 777 3 799 3 07 4 3 3 65 4 7 3 3 3067 4 334 5 34 4 The fudel de shpe is shw i Figure B-. The crrespdig ji ccepce fuci is shw i Figure B-. Nw pply he sud pressure level fr Mil-Sd-540C i Figure B-3 gle f 45. The resulig displcee d sress he ceer f he ple re shw i Figures B-4 d B-5, respecively. 5
Figure B-. 6
Figure B-. 7
Figure B-3. 8
Figure B-4. Ceer f Ple, 45 degrees Icidece 9
Figure B-5. Ceer f Ple, 45 degrees Icidece 0
APPENDIX C iiig Cse, Uifr Pressure Recll Fr, Â b (C-) / (C-) The pressure field beces uifr d rl s I his cse, 0,. Â b (C-3) The fllwig equi is equivle (C-3) fr s ieger d igrig he plriy shif. Â b (C-4) Equi (C-4) is esseilly siilr he resul fr uifr, rl pressure i Referece 4, llwce fr differece i he wy h he ss desiy ws ccued fr.