Undamped Free Vibration Solver

The undamped free vibration solver allows for solving undamped free vibration eigenvalue problems to determine eigenfrequencies and eigenmodes. It is invoked by the MDL command analysis free_vibration; this command must be specified in the case block.

[Note] Note

When executing B2000++, errors of the following kind

CRITICAL:all:16:22:8.124: Uncovered b2000 exception caught in the main function.
Exception: Error with the arpack subroutine aupd, info = -9.

are often indicative of missing density specifications in the material definitions.

[Note] Note

When executing B2000++, warnings of the following kind

WARNING:solver.eigenvalue.arpack:12:36:35.234: Maximum number of iterations taken.
All possible eigenvalues (0) have been found.

are indicative that the value for the nmodes option should be increased.

1. MDL Commands

In addition to the MDL command analysis free_vibration, the following commands may be specified in the case block.

m_orthonormal yes|no

If the mode shapes should be normalised w.r.t. the mass. Default is no (meaning that the mode shapes are normalised w.r.t. unit length).

nmodes v

Number of free-vibration modes v to be computed (default: 1). It is often necessary to set this option to values of 10 or even 20 for the successful solution of the eigenvalue problem.

shift v

The spectral frequency (not the circular frequency!) shift value. The computed free-vibration modes are the ones whose eigen-frequency is near this value. Default is 0. For complex problems, a complex spectral frequency shift value can be provided.

which_eigenvalues v

Indicates where to search for eigenvalues with respect to 0 or to the current shift value. sm searches for the smallest eigenvalues around 0 or the current shift value (default). la searches for the smallest eigenvalues to the left of 0 or the current shift value. ra searches for the smallest eigenvalues to the right of 0 or the current shift value.