(二)例 例↑磁致伸缩换能器一两端自由得均匀细杆 自由:振动传递给外界 u -a u XX l,(x,1)==0(xD)==0 1=0=9(x)u(x)=0=v(x) A.分离变量:v(x,1)=Y(x)(1)x,-a2xT=0 X"(O)7()=0X()7(t)=0 T+ha T=0 X(0)=0和X(D)=0 X+X=0 X(x)=C1cos√x+C2si AC2=0 n丌 n=0,1,2,3 √A(-C1sn√a+C2cos)=0（二）例 例1 磁致伸缩换能器－两端自由得均匀细杆。 自由：振动传递给外界 0 2 utt − a uxx = 0 l x ux (x,t) x=l = 0 ux (x,t) x=l = 0 ( ) 0 u x t= = ( ) ( ) 0 u x x t t= = A. u(x,t) = X (x)T(t) '' '' 0 2 XT −a X T = X '(0)T(t) = 0 X '(l)T(t) = 0 分离变量： '' 0; 2 T +a T = X ''+X = 0; X '(0) = 0 和 X '(l) = 0. X (x) C cos  x C sin  x B. = 1 + 2 0, C2 =  (−C1 sin l +C2 cos l) = 0 2 2 2 l n   = n = 0,1,2,3 