特解及一般解 因此,既满足 Laplace方程、又满足齐次边界条件 的特解为 un(,y)= C, sinb 2n+1 2n+1 ny+Dn cosh 2n+1 X SIn T 20
Steady State Problems Forced Vibration in a String Fixed at Both Ends A)9) Ïd§Q÷vLaplace§!q÷vàg>.^ A) un(x, y) = Cn sinh 2n+1 2a πy+Dn cosh 2n+1 2a πy × sin 2n+1 2a πx C. S. Wu 1nù ©lCþ{()
特解及一般解 因此,既满足 Laplace方程、又满足齐次边界条件 的特解为 un(,y)= C, sinb 2n+1 2n+1 ny+Dn cosh 2n+1 X SIn T 20 将这无穷多个特解叠加起来,就得到一般解
Steady State Problems Forced Vibration in a String Fixed at Both Ends A)9) Ïd§Q÷vLaplace§!q÷vàg>.^ A) un(x, y) = Cn sinh 2n+1 2a πy+Dn cosh 2n+1 2a πy × sin 2n+1 2a πx òùáõA)U\å5§Ò) C. S. Wu 1nù ©lCþ{()
特解及一般解 2a //+Dn cosh <n+1 Cn sinh <n+1 T 2n+1 X SIn
Steady State Problems Forced Vibration in a String Fixed at Both Ends A)9) u(x, y)=X ∞ n=0" Cn sinh 2n+1 2a πy+Dn cosh 2n+1 2a πy × sin 2n+1 2a πx # C. S. Wu 1nù ©lCþ{()
利用本征函数的正交性定叠加系数 代入关于y的一对(非齐次)边界条件 2n+1 D sin 2a7t=f(a) 2n+1 2n+1 y n=o 2 Cn,cosh 20 7b 2n+1 2n+1 +Dn sinh Tt0 sIn 2a x=0 根据本征函数的正交归一性
Steady State Problems Forced Vibration in a String Fixed at Both Ends |^ ¼ê5½U\Xê \'uyé(àg)>.^ u y=0 = X ∞ n=0 Dn sin 2n + 1 2a πx = f(x) ∂u ∂y y=b = X ∞ n=0 2n + 1 2a π Cn cosh 2n + 1 2a πb + Dn sinh 2n + 1 2a πb sin 2n + 1 2a πx = 0 â ¼ê85 Z a 0 sin 2n + 1 2a πx sin 2m + 1 2a πxdx = a 2 δnm C. S. Wu 1nù ©lCþ{()
利用本征函数的正交性定叠加系数 代入关于y的一对(非齐次)边界条件 2n+1 D sin 2a7t=f(a) 2n+1 2n+1 y n=o 2 Cn,cosh 20 7b 2n+1 2n+1 +Dn sinh Tt0 sIn 2a x=0 根据本征函数的正交归一性 n+1 2m+1 SIn 7t r sIn and 2a
Steady State Problems Forced Vibration in a String Fixed at Both Ends |^ ¼ê5½U\Xê \'uyé(àg)>.^ u y=0 = X ∞ n=0 Dn sin 2n + 1 2a πx = f(x) ∂u ∂y y=b = X ∞ n=0 2n + 1 2a π Cn cosh 2n + 1 2a πb + Dn sinh 2n + 1 2a πb sin 2n + 1 2a πx = 0 â ¼ê85 Z a 0 sin 2n + 1 2a πx sin 2m + 1 2a πxdx = a 2 δnm C. S. Wu 1nù ©lCþ{()