https://github.com/j-jith/fsrk-rom

Frequency domain reduced order model (ROM) for second-order systems with frequency dependent matrices
https://github.com/j-jith/fsrk-rom

model-order-reduction

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Frequency domain reduced order model (ROM) for second-order systems with frequency dependent matrices

• Host: GitHub
• URL: https://github.com/j-jith/fsrk-rom
• Owner: j-jith
• License: mit
• Created: 2018-03-13T14:00:36.000Z (almost 7 years ago)
• Default Branch: master
• Last Pushed: 2018-03-13T14:02:53.000Z (almost 7 years ago)
• Last Synced: 2023-10-19T18:54:05.243Z (about 1 year ago)
• Topics: model-order-reduction
• Language: Python
• Homepage:
• Size: 7.81 KB
• Stars: 0
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.rst
  • License: LICENSE

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README

        
This repository consists of a Python implementation of a frequency domain

Reduced Order Model (ROM) for second-order systems with frequency dependent

system matrices, called Frequency dependent second-order Rational Krylov

(FSRK) [jith2018]_.

It can be applied to systems of the form

.. math::

   -\omega^2 M(\omega) x + i \omega C(\omega) x + K(\omega) x = f,

where :math:`M, C, K` are *frequency dependent* mass, damping and stiffness

matrices.

FSRK ROM is implemented as a class in the file ``fsrk.py``. The current

implementation was made for systems with non-viscous damping. Therefore, it

only considers the damping matrix to be frequency dependent. It can be easily

extended if needed (feel free to open up an issue).

The usage of the ROM has been demonstrated in ``main.py``. A toy problem

consisting of serially connected spring-mass-damper units (of order 500) is

reduced using the FSRK ROM. The performance of the ROM is compared with the

existing modal projection based multi-model ROM (``multimodel.py``)

[balmes1997]_.

References

----------

.. [jith2018] Jith J. and Sarkar S. A Frequency Domain Model Order Reduction

   Technique for Second-Order Systems with Nonlinear Frequency Dependent

   Damping. Submitted to Computer methods in Applied Mechanics and Engineering,

   2018.

.. [balmes1997] Balmès E. Model Reduction for Systems with Frequency Dependent

   Damping Properties. Proceedings of the 15th International Modal Analysis

   Conference, vol. 3089, 1997, p. 223.