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On Gramian-Based Techniques for Minimal Realization of Large-Scale Mechanical Systems

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Topics in Modal Analysis, Volume 7

Abstract

Abstract In this paper, a review of Gramian-based minimal realization algorithms is presented, several comments regarding their properties are given and the ill-condition and efficiency that arise in balancing of large-scale realizations is being addressed. A new algorithm to treat non-minimal realization of very large second-order systems with dense clusters of close eigenvalues is proposed. The method benefits the effectiveness of balancing techniques in treating of non-minimal realizations in combination with the computational efficiency of modal techniques to treat large-scale problems.

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Notes

  1. 1.

    The \(\mathcal{L}_{p}\) norm is the Lebesgue spaces p-norm defined for real-valued functions.

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Authors and Affiliations

  1. Department of Applied Mechanics, Chalmers University of Technology, SE-41296, Gothenburg, Sweden

    Sadegh Rahrovani, Majid Khorsand Vakilzadeh & Thomas Abrahamsson

Authors
  1. Sadegh Rahrovani
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  2. Majid Khorsand Vakilzadeh
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  3. Thomas Abrahamsson
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Corresponding author

Correspondence to Sadegh Rahrovani .

Editor information

Editors and Affiliations

  1. University of Cincinnati, Cincinnati, 45221-0018, Ohio, USA

    Randall Allemang

  2. , The Enterprise Program, Michigan Technological University, Townsend Drive 1400, Houghton, 49931, Mississippi, USA

    James De Clerck

  3. , Dept. of Mechanical Engineering, University of Massachusetts Lowell, Riverside St. 197, Lowell, 01854, Massachusetts, USA

    Christopher Niezrecki

  4. & State University, Department of Mechanical Engineering, Virginia Polytechnic Institute, Randolph Hall 114 T, Blacksburg, 24060, Virginia, USA

    Alfred Wicks

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© 2014 The Society for Experimental Mechanics

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Rahrovani, S., Vakilzadeh, M.K., Abrahamsson, T. (2014). On Gramian-Based Techniques for Minimal Realization of Large-Scale Mechanical Systems. In: Allemang, R., De Clerck, J., Niezrecki, C., Wicks, A. (eds) Topics in Modal Analysis, Volume 7. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6585-0_75

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  • DOI: https://doi.org/10.1007/978-1-4614-6585-0_75

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6584-3

  • Online ISBN: 978-1-4614-6585-0

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