## Frequency-Dependent Undamped Free-Vibration Solver (B2000++ Pro)

The frequency-dependent undamped vibration solver allows for solving frequency-dependent free vibration eigenvalue problems to determine eigenfrequencies and eigenmodes, where the linear internal forces and internal inertia are frequency-dependent. It is invoked by the MDL command analysis frequency_dependent_free_vibration; this command must be specified in the case block.

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 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 frequency_dependent_free_vibration, the following commands may be specified in the case block.

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 shift value. The computed free-vibration modes are the ones whose eigen-frequencies are near this value (default=0). For complex problems, a complex spectral frequency shift value can be provided.

freq_init v

The initial frequency used in the first stage of the algorithm.

tol v

The relative tolerance of the computation of the exact eigenfrequency.

tol_predictor v

The relative tolerance for the re-computation of the approximated eigenfrequencies.