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1 RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revisio E B To Ivie Eil: o@viiod.co Apil, 3 Viles A pliude coefficie E k leg id ple siffess fco elsic odulus ple ickess veue ple ss edig oe,, u, v ode ue idices Poisso's io ss pe volue elive displcee, ou-of-ple olied ode spe picipio fco eciio feuec ul feuec odl dpig () W( ) elive displcee, ou-of-ple se ipu cceleio Fouie sfo of se ipu cceleio (,, ) Relive displcee U (,, ) Asolue Acceleio

2 Ioducio Coside e ecgul ple i Figue. Assue i is sipl-suppoed log ec edge. Y X Figue. Nol odes Alsis Noe e ple siffess fco is give E 3 () Te goveig euio of oio is () Assue oic espose. (,,) (, )ep( j) (3)

3 3 ) ep( j ) ep( j () (5) Te oud codiios e (,), (,) fo =, (6) ) (,, ) (, fo =, (7) Assue e folloig displcee fucio ic sisfies e oud codiios, ee c is pliude coefficie d e ieges. si A si (,) (8) Te pil deives e si cos A (9) si si A () si cos A ()

4 si si A () Siill, si si A (3) Also, si si A () si si A si si A (5) (6) (7) (8)

5 5 (9) Noe e ve ues e / k () / k () Nolied ode Spes Te ode spes e olied suc d d (,) () si A si (3) d d si A si () d d si si A (5) d d cos cos A (6)

6 (7) cos si d A (8) cos d A si A (9) A (3) A (3) A A (3) (33) (3) A (35) Noe A is cosideed o e diesioless, loug e uis us e cosise ii e lsis. 6

7 7 Picipio Fcos Te ss desi is cos. Tus (,)d d (36) d d si A si (37) d d si si A (38) d d si si (39) d si cos () d si cos () cos cos () cos cos (3)

8 cos cos () cos cos (5) Effecive odl ss (, )d d eff, (6) )d d (, Te odes spes e olied suc Tus (,)dd (7) eff, )d d (, (8) eff, (9) 8

9 9 Respose o Bse Eciio Te foced espose euio fo ple i se oio is (5) ee is se eciio. Te e o e ig-d-side is e ieil foce pe ui e. Te displcee is T () ) (,,) (, (5) si si (,) (5) (53)

10 T () ) (, T () ) (, T () ) (, T () ) (, (5)

11 T () ) (, T () ) (, T () ) (, T () ) (, (55) si si (,) (56) si si ) (, (57) ) (, ) (, (58) si si ) (, (59)

12 si si ) (, (6) ) (, ) (, (6) si si ) (, (6) si si ) (, (63) ) (, ) (, (6) T () ) (, T () ) (, T () ) (, T () ) (, (65)

13 3 T () ) (, T () ) (, (66) T () ) (, T () ) (, (67) T () ) (, T () ) (, (68)

14 ulipl ec e uv(, ). uv(, ) (, ) T () uv(, ) (, ) T () uv(, ) (69) Iege i espec o sufce e. uv (, ) (, ) T () dd uv (, ) (, ) T () dd uv (, ) dd (7)

15 5 )d d ) (, uv (, T () )d d ) (, uv (, T () ) uv (, (7) Te eigevecos e oogol suc uv (,) (,)d d fo u o v (7) uv (,) (,)dd fo u = d v = (73)

16 T () T () (, )d d (7) T () T () (, )d d (75) d d T () d T () (76) d Add dpig e. d d T () d T () T () (77) d T () T () T () () (78) 6

17 Te folloig soluio is ke fo Refeece 3. Te sfe fucio is (, ) H (,, ) (79) ( ) j H(,, ) (,, ) W (8) Te elive displcee is (, ) (,, ) W (8) ( ) j (,, ) si si W (8) ( ) j Te elive veloci is (, ) (,, ) j W ( (83) ) j si si (,, ) j W ( (8) ) j 7

18 Te solue cceleio is (, ) U (,, ) W (85) ( ) j si si U (,, ) W (86) ( ) j Te edig oes e,,,, (87),,,, (88) Le ẑ e e disce fo e ceelie i e veicl is. Te edig sesses fo Refeece e E ẑ,,,, (89) 8

19 E ẑ W,, (, ) ( ) j (9) E ẑ,, W si si ( ) j (9) E ẑ,,,, (9) E ẑ W,, (, ) ( ) j (93) E ẑ,, W si si ( ) j (9) 9

20 E ẑ,,,, (95) (, ) E ẑ W (96) ( ) j,, E ẑ W,, cos cos ( ) j (97) Refeeces. ve Seieg, Viio Alsis fo Elecoic Euipe, Wile-Iesciece, Ne Yok, Au W. Leiss, Viio of Ples, NASA SP-6, Niol Aeouics d Spce Adiisio, Wsigo.C., T. Ivie, Sed-Se Viio Respose of Cileve Be Sujeced o Bse Eciio Revisio A, Viiod, 9.. J.S. Ro, ics of Ples, Nos, Ne eli, 999.

21 APPENIX A Nol Sess-Veloci Reliosip Te iu solue spil sesses fo give ode, e, E ẑ W ( ) j (A-), E ẑ W ( ) j (A-) Te iu spil veloci fo give ode, is W (A-3) ( ) j Tus E ẑ, (A-) E ẑ, (A-5)

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