MT-16.20 al.2002 Recall the governing equation W el- t p dx dx Notice that p does not enter into the equation on the right hand side(making the differential equation homogenous), but enters as a coefficient of a linear differential term This is an eigenvalue problem. Let W=已 this gives EI i0.0 E epeated roots= need to look for more solutions End up with the following general homogenous solution W= Asin-x+ Bcos -x+C+ Dx El Paul A Lagace @2001 Unit 16-9MIT - 16.20 Fall, 2002 Recall the governing equation: 4 2 EI dw + P dw = 0 dx 4 dx2 --> Notice that P does not enter into the equation on the right hand side (making the differential equation homogenous), but enters as a coefficient of a linear differential term This is an eigenvalue problem. Let: λ x w = e this gives: λ4 + P λ2 = 0 EI ⇒ λ = ± P EI i 0, 0 repeated roots ⇒ need to look for more solutions End up with the following general homogenous solution: w = Asin P EI x + B cos P EI x + C + Dx Paul A. Lagace © 2001 Unit 16 - 9