- #1

- 63

- 0

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,