How do I solve an eigenvector for the amplitude matrix 'A' mode

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Derek Burnside 2020-4-22

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评论： Derek Burnside 2020-4-22

Assuming a simpified equation A*B = 0, where 'B' is known and is a 10x10 (numercial) matrix and 'A' is not known and is a 1x10 matrix (A1, A2...........A10). Trying to solve for A1, A2, etc to eventually draw a mode shape.

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Derek Burnside 2020-4-22

Thanks Giafari, yes it is mass and stiffness problem, but just looking for a simple solution to solve for ‘A’. Where A*B=0 and B is a 10x10 matrix with numerical values and A is a 1x10 matrix (A1 A2 ....).

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Answer 1

Gifari Zulkarnaen 2020-4-22

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Are you trying to make eigendecomposition of mass & stiffness matrix? Try this:

[U,Omega2] = eig(inv(M)*K);      % Eigen decomposition
[omg2,ind] = sort(diag(Omega2)); % Sort the order of modes based on their natural frequency
Omega2 = Omega2(ind,ind);
U = U(:,ind);                    % Mode shapes matrix
omg_n = sqrt(omg2);              % Natural radial frequencies