q=0 =0(0≤y<b)(1) =0(0≤y<b)(2) 。=0(0≤x≤a)() b b=U(0≤x≤a)(4) P=(A*+bo(coy+do)t >IA, sin(k, x)+B, cos(k, x)ICn sh(km, 3)+D, ch(kny)] 由条件(1)→B=0,B.=0 由条件(2)→A=0,kn=(n=1,2…) 由条件(3)→D=0 P=2A'n sin(-/x)sh(y)(A, =A,Cn) 由条件(4) l=∑ A sind("x)s(b)2 = 0 0 0 (0 ) (1) x y b = = 0 (0 ) (2) x a y b = = 0 0 (0 ) (3) y x a = = (0 ) (4) y b U x a = = x y a b = u 0 0 0 0 ( )( ) [ sin( ) cos( )][ ( ) ( )] n n n n n n n n A x B C y D A k x B k x C sh k y D ch k y = + + + + n=1 + 由条件(1) 0 0, 0 = = B B n 由条件(2) 0 0, ( 1,2, ) n n A k n a = = = 由条件(3) 0 = D n ' ' sin( ) ( ) ( ) n n n n n n A x sh y A A C a a = = n=1 由条件(4) ' sin( ) ( ) n n n u A x sh b a a = n=1