1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Eigenvalue problem

  1. Apr 14, 2013 #1
    Eigenvalue problem after galerkin

    1. The problem statement, all variables and given/known data

    i am working on vibration of cylindrical shell analysis, after solving the equations of motion by galerkin method , i reach to an eigenvalue problem this way :

    { p^2*C1+p*C2+C3 } * X=0

    C1,C2,C3 are all square matrices of order n*n and all are known ones, and X is a vector of unknown coeffs.

    now for nontrivial solution, the determinant of the coefficient matrix must vanish:


    which should be reduced to a standard eigenvalue problem by transferring to state-space as:



    M=[-(C1^-1)*C2 , I ; -(C1^-1)*C3 , 0]

    where I is the identity matrix of order (n*n) and M is a (2n*2n) matrix.

    2. Relevant equations

    3. The attempt at a solution

    now i must find the eigenvalues of matrix M which is expected to be the values of p

    also there is an alternative way for finding p , which is solving det(p^2*C1+p*C2+C3) in terms of p and getting the roots ,

    my problem is that these two methods don't give exactly the same answers , they're similar but some p values are different , for example after soving the det(p^2*C1+p*C2+C3) the result is :

    0.1204 + 370.8*i
    - 4.264 - 394.2*i
    - 8.648 + 370.8*i
    - 4.264 + 506.2*i
    - 4.264 - 506.2*i
    - 4.264 + 394.2*i
    0.1204 - 370.8*i
    - 4.264 - 443.6*i
    - 4.264 + 443.6*i
    - 8.648 - 370.8*i

    but when i get eigenvalue of M matrix in matlab , i see:

    1.0e+02 *

    -0.0426 + 3.6016i
    -0.0426 + 5.0844i
    -0.0426 - 3.6016i
    -0.0426 + 3.9915i
    -0.0426 - 5.0844i
    -0.0426 + 4.4363i
    -0.0426 + 3.7287i
    -0.0426 - 3.9915i
    -0.0426 - 4.4363i
    -0.0426 - 3.7287i

    in matlab one time i write eig(M) to find eigenvalues , and one time i do this way:

    solve(det(p^2*C1+p*C2+C3) , p)

    also all p values are expected to be complex and they are . the values taken by two methods are simillar in some values but are totally different in others.

    i don't know why these two are not the same !

    PLEASE HELP me !! thanks in advance
    Last edited: Apr 14, 2013
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted