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## Main Question or Discussion Point

hi community,

In general I would like to know the what's the general way of solving the moderate or large-scale eigenvalue or algorithms in structural dynmics.

The simple motion equation is as follow.

The bolded expressions are known before the equation solution , mass, damping, stiffness and loading matrix, respectively, so those are known values either time-dependent or constant.

Solution of above equation, including various combinations, e.g. undamped-damped system, constant force, time dependent force etc.., has been given in books, in most of them eigenvalue has been introduced or transformed to A*λ=X*λ form. Among the solution methods it's been mentioned that, power method, eigenvalue decomposition, householder reflectionm, sturm secuence, Wielandt deflation etc.. are most effective, they usually introduce an

My question is: Since I have M,C,K,F(t) four matrices how to convert them into A-matrix form, depending on the problem type, in order to commence the solution for the fore-mentioned methods?

Regards,

In general I would like to know the what's the general way of solving the moderate or large-scale eigenvalue or algorithms in structural dynmics.

The simple motion equation is as follow.

**M***d^{2}X(t)/dt^{2}+**C***dX(t)/dt+**K***X(t) =**F(t)**.The bolded expressions are known before the equation solution , mass, damping, stiffness and loading matrix, respectively, so those are known values either time-dependent or constant.

Solution of above equation, including various combinations, e.g. undamped-damped system, constant force, time dependent force etc.., has been given in books, in most of them eigenvalue has been introduced or transformed to A*λ=X*λ form. Among the solution methods it's been mentioned that, power method, eigenvalue decomposition, householder reflectionm, sturm secuence, Wielandt deflation etc.. are most effective, they usually introduce an

**A**matrix and trying to find the eigenvalues and eigenvectors of it.My question is: Since I have M,C,K,F(t) four matrices how to convert them into A-matrix form, depending on the problem type, in order to commence the solution for the fore-mentioned methods?

Regards,