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HomeWork7 - HW#7 1 a q0 x x a z qo a4 wmax = = 0.0020932 at...

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HW#7 1. 2. (a) Find the expression for R . (b) If 2 o R q a α = , find α . Take a minimum of 4 terms in the summation. 0.1868, for 9 terms α B 0.18538 α B , for 16 terms 1 0 q y a x x z a 4 max , 0.0020932, at 0.55 , 0.5 o q a w x a y a D α α = = = = y 4 a 2 a 4 a 4 a 0 q R x R 4 a 2 a x x x x
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Solution for 2. From Eq. (4-39) ( 29 ( 29 0 0 2 2 0 0 0 2 4 4 sin sin cos cos 0 0 4 cos 1 cos 1 a a mn a a q q m x n y a m x a n y a dxdy a a a a m a n a q m n mn π π π π π π π π π  = =   = - - ∫ ∫ From Eq. (4-37), 2 4 2 2 1 1 2 2 1 sin sin mn m n a m x n y w D a b m n a b π π π = = = + ∑∑ . At and 4 4 a a x y = = , the deflection is ( 29 0 4 4 0 2 4 2 2 1,3,5 1,3,5 sin sin 4 4 0.0021329 q mn m n m n q a a w a D D m n π π π = = = = + ∑ ∑ from Maple ® for m=1,3,5 and n=1,3,5 From Eq. (4-42) 2 4 sin sin with and 4 4 mn P m n a a a a a a πξ πη ξ η = = = ( 29 4 1 2 4 2 2 1 1 sin sin with and 4 4 mn c m n a a m x n y a a w x y D a a m n π π π = = = = = + ∑∑ ( 29 4 2 2 4 2 2 1 1 3 sin sin with and 4 4 mn c m n a a m x n y a a w x y D a a m n π π π = = = = = + ∑∑ ( 29 4 3 2 4 2 2 1 1 3 sin sin with and 4 4 mn c m n a a m x n y a a w x y D a a m n π π π = = = = = + ∑∑ ( 29 4 4 2 4 2 2 1 1 3 3 sin sin with and 4 4 mn c m n a a m x n y a a w x y D a a m n π π π = = =
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