ANALY SIS OF NONL INEAR DY NAM IC SOL ID -FL U ID INTERACTION RESPONSE OF A LAM INATED COM POSITE PLATE

Transcription

1 A CTA M A T ER IA E COM PO S ITA E S IN ICA V o. 7 N o. February 2000 : (2000) (, ) : ; H am ton ; ; : ; ; ; : TB 330. : A ANALY SIS OF NONL INEAR DY NAM IC SOL ID -FL U ID INTERACTION RESPONSE OF A LAM INATED COM POSITE PLATE TAN G W en2yong ZHAN G Sheng2kun CH EN T e2yun (Schoo of N ava A rch tecture and O cean Engneerng, Shangha J ao Tong U nversty, Shangha , Ch na) Abstract: T he app rox m ate exp resson of the fu d fo rce betw een a foatng am nated compo ste p ate and qu d su rface s ob taned n th s paper. N on near dynam c equaton s ncudng the effects of tran sverse shear defo rm aton and so d2fu d n teracton are estab shed by H am ton s p rncp e. T he non near dynam c so d2fu d n teracton respon se s so ved by m ean s of a dfference m ethod. T he effects of non2nearty and fu d dep th under dfferen t oadng fo rm s on dynam c respon se are dscu ssed. Key words: compo ste structu re; am nated p ate; so d2fu d n teracton; dynam c respon se,,, R am achandra [ ] ; [2, 3 ],,,,., y, F g. L am nated compo ste p ate on fud surface : ; : : ( ) : (970),,,,.

2 94 2, h, H,, x, x Υ, θ u (x, z, t) = u (x, t) + z Α(x, t) w { (x, z, t) = w (x, t) () : u, w, Α y Εx = Ε (0) x + z k x, Χx z = Α+ Ε (0) x = 5u, k x = 5Α (2) 2 q f,, H am ton 5M x = Θh 52 u + N x N x = A M x = B 5 2 w 2 + 5Q x - Q x = 2 Θh 3 52 Α 5u 5u Q x = Α q f + q = Θh 52 w + B + D (A, B, D ) = hg2 (k) Qϖ - hg2 = : Q ϖ (k) n p 5 4 Q ϖ 55 (k) z k - z k- - 5Α 5Α (, z, z 2 ) dz 4 3h 2 (z 2 k - z 2 k- ) (3) (4) Q ϖ 55 (k) k, np. 2, : () ; (2) ; (3) 8 E, 8 E28 I (), 5, 2 5 (x, z, t) = 0 (5) 8 E= 8 E+ 8 E2, 55 E 5 Eg 0, gx g> = 0, 5 Eg gx g = 0, = 0 (6) 5z z = - H, 8 E 8 E2 5 E = A n (t) e Κ n x sn Κnz (7) 5 E2 = A 2n (t) e - Κ n x sn Κnz (2n- ) Π, Κn= 8 I, 2H = 0 (8) 5z z = - H 5 I= F (x )G (z ), F (x ) F (x ) = - 8 I G (z ) G (z ) = - Β2 (9) 5 I = (B co s Βx + B 2sn Βx ) ch Β(z + H ) (0) e Κ n gx g Κn g x g,, (7) [4 ], 55 E x = =, 5 Egx= = 5 Ig x = () z = A e - Κ sn Κz = (B co s Β - B 2sn Β) ch Β(z + H ) A Κe - Κ sn Κz = Β(B sn Β + B 2co s Β) ch Β(z + H ) A 2e - Κ sn Κz = (B co s Β - B 2sn Β) ch Β(z + H ) A 2Κe - Κ sn Κz = Β(B sn Β - B 2co s Β) ch Β(z + H ) (2) A A 2 B B 2, Β (Κco s Β - Βsn Β) (Κsn Β + Βco s Β) = 0 (3), Β, Κco s Β- Βsn Β = 0 B 2= 0; Κsn Β+ Βco s Β= 0 B = 0, 5 I = [B n (t) co sβn (z + H ) + B 2n (t) snβ2nx ch Β2n (z + H ) ] (4), Βn Β2n co sβm x co sβnx dx = - snβ2m x snβ2nx dx = - Κco s Βn = Βn sn Βn ; - Κsn Β2n = Β2nco s Β2n (5) 0 m n + 2H Π sn2 Βn m = n 0 m n + 2H Π co s2 Β2n m = n (6a) (6b)

3 , : 95 co sβm x snβ2nx dx = 0-5z z = 0, gx g = 5t (6c) (7) [ΒnB n (t) shβnh co s Βnx + Β2nB 2n (t) shβ2nh sn Β2nx ] = w α (x, t) (8) (6), B nb 2n w α (x, t) co sβnx dx - B n (t) = Βn sh (ΒnH ) + 2H Π sn 2 Βn w α (9) (x, t) snβ2nx dx - B 2n (t) = Β2n sh (Β2nH ) + 2H Π co s2 Β2n (4), 5 I q f = - Θ 0 5t z = 0 q f = - Θ 0 Πcth (ΒnH ) Πcth (Β2nH ) - wβ (x, t) co s (Βnx ) dx Βn[Π + 2H sn 2 (Βn) ] - wβ (x, t) sn (Β2nx ) dx Β2n[Π + 2H co s 2 (Β2n) ] : Θ 0,w β = 5 2 w g 2 (3) : co s (Βnx ) + (20) sn (Β2nx ) (2) [M ]{X β } + [K ]{X } + [G ]{X } = {F } (22) : {X }= {u,w, Α, N x,m x, Q x } T, {F }= {0, q f + q, 0, 0, 0, 0} T, () = 5() g5t : m = m 22 = Θh, m 33 = 2 Θh3, k 4 = k 26 = k 35 = -, k 24= -, k 4= A, k 42= 2 A, k 43= k 5= B, k 52= 2 B, k 53 = D, k 62 =, g 24 = 5 Α- Q x, g 36=, g 44= g 55= g 66= -, g 63= (22), {X } j - g2 = 2 {X } j - {X } j - {X } j - g2 = 2 {X }j + {X } j - {X β } j - g2 = 2 {Xβ } j + {X β } j - (23) : j, Park [5 ], {X α } j = 6 ( t) (0{X } j - 5{X } j- + 6{X } j- 2 - {X } j- 3 ) (24) (22), Κr (x ) = Κ2r (x ) = Θ0cth (ΒrH ) co s (Βrx ) Βr + 2H Π sn2 (Βr) Θ0cth (Β2rH ) sn (Β2rx ) Β2r + 2H Π co s2 (Β2r), r=, 2, 3,, q f = - r= [Κr (x ) - w β (x, t) co s (Βrx ) dx + () Κ2r (x ) w β (x, t) sn (Β2rx ) dx ] (26) -, N S,,, q f (- g2) = N S + (+ k) β - g2w k- g2 (27) + k= r= [Κr (x ) co s (Βrx k- g2) + Κ2r (x ) sn (Β2rx k- g2) ] (22), j {X } j (s) = {X } {X } j (0) j (s- ) j- (s) = {X } + { X } j (s) (28) : s, ( 23) (28) (22), j (s- ) [H ] - g2 { X } j - (s) j (s- ) + [H 2 ] - g2 { X } j (s) { Y } j (s) = {R } + j (s- ) - g2 (29), =, 2,, N S+, [H ] = [H 2 ] = { Y } = 0, 8 ( t) 2 [M ] - ([K ] + [ K 3 ] + [G 3 ]) + 2 [G ] 8 ( t) 2 [M ] + ([K ] + [ K 3 ] + [G 3 ]) + 2 [G ] N S + 8 ( t) (+ 2 k+ + k+ ) w k, 0, 0, 0, 0 {R }= {F }- [M ]{X β }- [K ]{X }- [G ]{X } [K 3 ] [G 3 ][K ] [G ] k 24= - k 42= 2 A k 52= 2 B g 24= T

4 96 5 Α- Q x (28), : k 3 22= - 2 B, g 3 23= N x, g 3 26= -, k 3 42= 2 A, k 3 52= N x { X } j (s) 0-7 {X } j (x ) (30), : {X } 0 = {0}, {X α } 0 = {0}; (22) : q = q m ( - tgtd) e - Α 0 tgt d 0 t td 0 t > td (3) : q m, td, Α0 3,, q (3), (4 5),,, 3 g, E = 206 GPa, E 2= 0. 3 GPa, G 2= G 3= 6. 2 GPa, G 23 = 4. 3 GPa, Μ2= 0. 28, Θ= 600 kggm 3 u= w = Α= 0: = 0. 3 m, h= m ; Θ 0 = 000 kggm 3, H = 0 ;, Υ= 30, 40,,. 0 kn gm 2 ;, 0 kn gm 2,. 98 2, gw (0) gm ax, 3( ) F g. 3D sp acem ent response fo r fxed edges(step oad) 4(td= 0. 0 s) F g. 4D sp acem ent response under exp o sve oad (td= 0. 0 s) 2 ( ) F g. 2D sp acem ent response under dfferent oads(fxed edges) 5(td= s) F g. 5D sp acem ent response under exp o sve oad (td= s)

5 , : 97 [ ]Ram achandra L S, M eyer2p enng H 2R. T ransent response of sandw ch p ates n contact w th w ater [ J ]. 996, 60 (4) : Comp ut S truct, [ 2 ],,. [J ]., 996, 3 (3) : [ 3 ],,,. [J ]., 994, (4) : [ 4 ] Zhu F. N on2near vbratons of a foatng beam under harmonc exctaton [J ] J S ound V b, 994, 72 (4) : 689 [ 5 ] Park K C. A n mp roved stffy stabe m ethod fo r drect ntegraton of nonnear structura dynam cs equatons [J ]. A pp M ech, 975, 42 (3) : J