分离变量 a2u a2u 0<x<a,0<y<b au =00<y<b =00<x<a X"(x) X(x)+λX(x)=0 X() Y"(y)-AY(y)=0 代入关于x的一对齐次边界条件
Steady State Problems Forced Vibration in a String Fixed at Both Ends ©lCþ ∂ 2u ∂x2 + ∂ 2u ∂y2 = 0 0<x< a, 0<y < b u x=0 = 0 ∂u ∂x x=a = 0 0≤y≤b u y=0 = f(x) ∂u ∂y y=b = 0 0≤x≤a X00(x) X(x) =− Y 00(y) Y (y) =−λ =⇒ X00(x)+λX(x)=0 Y 00(y)−λY (y)=0 ✑ \'uxéàg>.^ C. S. Wu 1nù ©lCþ{()
分离变量 a2u a2u 0<x<a,0<y<b au =00<y<b =00<x<a X"(x) X(x)Y(-x→ X(x)+λX(x)=0 Y"(y)-AY(y)=0 X(0)Y(y)=0 X(0)=0 X(ar(=0 X(a)=0
Steady State Problems Forced Vibration in a String Fixed at Both Ends ©lCþ ∂ 2u ∂x2 + ∂ 2u ∂y2 = 0 0<x< a, 0<y < b u x=0 = 0 ∂u ∂x x=a = 0 0≤y≤b u y=0 = f(x) ∂u ∂y y=b = 0 0≤x≤a X00(x) X(x) =− Y 00(y) Y (y) =−λ =⇒ X00(x)+λX(x)=0 Y 00(y)−λY (y)=0 X(0)Y (y)=0 X0 (a)Y (y)=0 =⇒ X(0)=0 X0 (a)=0 C. S. Wu 1nù ©lCþ{()
求解本征值问题 X a)+X(a)=0 X()=0X(a)=0
Steady State Problems Forced Vibration in a String Fixed at Both Ends ¦) ¯K X00(x) + λX(x) = 0 X(0) = 0 X0 (a) = 0 C. S. Wu 1nù ©lCþ{()
求解本征值问题 X a)+X(a)=0 X()=0X(a)=0 若入=0 微分方程的通解X(x)=Aox+B
Steady State Problems Forced Vibration in a String Fixed at Both Ends ¦) ¯K X00(x) + λX(x) = 0 X(0) = 0 X0 (a) = 0 ✑ eλ = 0 ©§Ï) X(x) = A0x + B0 C. S. Wu 1nù ©lCþ{()
求解本征值问题 X a)+X(a)=0 X()=0X(a)=0 若入=0 微分方程的通解X(x)=A0x+B0 边界条件=>0=0,B0=0
Steady State Problems Forced Vibration in a String Fixed at Both Ends ¦) ¯K X00(x) + λX(x) = 0 X(0) = 0 X0 (a) = 0 ✑ eλ = 0 ©§Ï) X(x) = A0x + B0 >.^ =⇒ A0 = 0, B0 = 0 C. S. Wu 1nù ©lCþ{()