Frequency
Last updated
Last updated
The (generalized) eigenvalue problem is handled in the Frequency
step. To define a valid step, please use the
following command.
To successfully run an eigen analysis, the system shall be symmetric, otherwise complex eigen values are computed. This typically requires the stiffness matrix to be symmetric. Besides, it must have
a positive definite stiffness matrix,
a semi-positive definite mass matrix.
The symmetric banded storage uses _pbsv
solver which only accepts symmetric positive definite banded matrix. If
the Frequency
fails to compute the required eigen modes, please use other storage schemes.
The computed eigenvalue is the eigenvalue of the system. In the field of structural dynamics, it is . The (angular) frequency and period can be computed accordingly.
The constrained (generalized) eigenvalue problems cannot be handled when the constraints are implemented via Lagrange multiplier method. If the system contains constraints, users shall make sure they are applied via the penalty function method.
By default, the ARPACK
solver is used to solve the generalized eigen problem.
The can also be used. To switch, one can use
Currently, the FEAST
solver can be applied to full, banded and sparse storage. For banded storage, it is necessary to
use the SPIKE
solver.
The output is
For the given centre and radius , the FEAST solver seeks eigenvalues within the bracket . If the radius is not assigned, it defaults to , thus the bracket becomes .
Consider a massless elastic cantilever beam with lumped end mass. Assume the length is , the elastic modulus is , the moment of inertia is and the lumped mass is so that