Sov method_id - Solution Procedure for the SOV Method 1 Assume F(x = i f x i Where F is the dependent variable x =[x1 x2 x3 xn is a vector of

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Solution Procedure for the SOV Method 1. Assume = i i x f F ) ( ) ( x Where: F is the dependent variable x = [x 1 x 2 x 3 …. x n ] is a vector of independent variables For example: ) ( ) ( ) , ( Fo h x g Fo x = θ 2. Substitute product into differential equation For example: Fo x = 2 2 h g hg = ' ' where g(x) only and h(Fo) only 3. Group terms containing the same independent variables by dividing by gh For example: h h g g gh h g gh hg = = ' ' ' ' 4. For the above to be true, each part is equal to a constant; therefore, introduce , which will become a set of eigenvalues, to satisfy the differential equation. 2 ζ For example: ) ( 2 ' ' ± = g g ) ( 2 ± = h h 5. Set up the corresponding ordinary differential equation (ODE). For example: 0 ) ( 2 ' ' = ± g g 0 ) ( 2 = ± h h 6. Choose the sign on the term such that a set of periodic orthogonal functions exists for the variable that has both homogeneous B.C.’s. 2
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For example: 1 ) 0 , ( ) , 1 ( 0 , 1 , 0 = = = = = x Fo Bi x x Fo x Fo x θ where x must be periodic This transforms to : 1 ) 0 ( ) 1 ( ) 1 ( 0 ) 0 ( = = = h g Bi g g
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This note was uploaded on 07/25/2008 for the course ME 410 taught by Professor Benard during the Spring '08 term at Michigan State University.

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Sov method_id - Solution Procedure for the SOV Method 1 Assume F(x = i f x i Where F is the dependent variable x =[x1 x2 x3 xn is a vector of

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