Vibration Generalized Eigenvalue Problem (GEP) helper functions.
Targeted at matrix pencils with real symmetric matrices. The GEP reads
(K - omega^2 * M) * v = 0
Here K is a symmetric, positive semi-definite, stiffness matrix, M is a symmetric positive definite mass matrix, omega is the angular velocity.
- Solve the vibration GEP for the smallest eigenvalues:
d, v, nconv = gep_smallest(K + omega_shift^2 * M, M, neigvs; method = :Arpack)
The solution is useful in constructing modal expansions in solid dynamics. It is
possible to select the method (package) to use, :KrylovKit, :Arpack, :ArnoldiMethod, and
:SubSIt are currently available.
- Solve the vibration GEP for the largest eigenvalue:
omega_max = gep_largest(K, M)
The solution is useful in estimating the stable time step in explicit integration of the equations of motion.