MIT2_092F09_hw8 - and K- orthogonal. b) Find (any) two...

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2.092/2.093± F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS F ALL 2009± Homework 8 Instructor: Prof. K. J. Bathe Assigned: Session 23 TA: Seounghyun Ham Due: Session 25 Problem 1 (20 points): Consider Problem 1 of Homework 7. a) Calculate the static correction to the analysis performed in Homework 7. b) Compare by plots the solutions obtained with (i) using one mode plus the static correction and (ii) using two modes, and discuss your results. Problem 2 (10 points): Establish a Rayleigh damping matrix C for the system of Problem 1 of Homework 7, which gives modal damping parameters, ξ 1 =0.02 and ξ 2 =0.10. Problem 3 (20 points): Consider the generalized eigenvalue problem 4 1 0 2 0 0 1 3 1 φ = λ 0 2 1 0 1 4 0 1 2 a)± Calculate the eigenvalues and eigenvectors and show explicitly that these vectors are M-
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Unformatted text preview: and K- orthogonal. b) Find (any) two vectors that are M- and K- orthogonal but are not eigenvectors. 1 Problem 4 (20 points): Consider the system in Problem 3. Perform two subspace iterations with the starting vectors 1 1 X 1 1 = 1 1 That is, calculate X 2 and X 3 , and hence the approximations to the exact eigenvalues and eigenvectors (obtained in Problem 3). 2 MIT OpenCourseWare http://ocw.mit.edu 2.092 / 2.093 Finite Element Analysis of Solids and Fluids I Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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MIT2_092F09_hw8 - and K- orthogonal. b) Find (any) two...

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