Resolution of the Generalized Eigenvalue Problem for symmetric matrices
The analysis of dynamical systems with multiple degrees of freedom leads to the following eigenvalue problem:
(K - λ M) u = 0.
The program calculates the eigenvalues λi and corresponding eigenvectors ui.
For dynamical systems of multiple degrees of freedom K is the stiffness matrix and M is the mass matrix.
The eigenfrequencies ωi of the modes of vibration can be calculated by means of ω2 = λ.
Required is that matrices M and Kare symmetric. In addition M must be positive definite
and the matrix of K must be positive semi-definite.