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An eigenvalue approximation for parameter-dependent undamped gyroscopic systems

An eigenvalue approximation for parameter-dependent undamped gyroscopic systems
An eigenvalue approximation for parameter-dependent undamped gyroscopic systems
Parameter–dependent eigenvalue problem occurs in a host of engineering contexts. Structural design under dynamic loading is concerned with the evaluation of eigenvalues for a large number of structures, each evaluation corresponding to a combination of design parameters. Exact calculation of the natural frequencies of all the models considered is computationally expensive. Here structural problems that possess gyroscopy, typically encountered in the analysis of rotating elastic structures, are considered. Approximate but inexpensive calculations are sought for this class of problems. In the present work, an algorithm for approximating the natural frequencies of undamped gyroscopic systems is presented. Numerical examples show excellent accuracy, while affording significant computational economy compared to exact calculations. The computational gain is found to be relatively more notable when the size of the considered problem is large.
1742-6596
Gavryliuk, Nataliia
220bff3d-794e-4480-977d-734a0ebc9e0e
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Gavryliuk, Nataliia
220bff3d-794e-4480-977d-734a0ebc9e0e
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e

Gavryliuk, Nataliia and Bhaskar, Atul (2018) An eigenvalue approximation for parameter-dependent undamped gyroscopic systems. Journal of Physics: Conference Series, 1106 (Conference 1), [012017]. (doi:10.1088/1742-6596/1106/1/012017).

Record type: Article

Abstract

Parameter–dependent eigenvalue problem occurs in a host of engineering contexts. Structural design under dynamic loading is concerned with the evaluation of eigenvalues for a large number of structures, each evaluation corresponding to a combination of design parameters. Exact calculation of the natural frequencies of all the models considered is computationally expensive. Here structural problems that possess gyroscopy, typically encountered in the analysis of rotating elastic structures, are considered. Approximate but inexpensive calculations are sought for this class of problems. In the present work, an algorithm for approximating the natural frequencies of undamped gyroscopic systems is presented. Numerical examples show excellent accuracy, while affording significant computational economy compared to exact calculations. The computational gain is found to be relatively more notable when the size of the considered problem is large.

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Accepted/In Press date: 14 September 2018
e-pub ahead of print date: 5 November 2018

Identifiers

Local EPrints ID: 426031
URI: http://eprints.soton.ac.uk/id/eprint/426031
ISSN: 1742-6596
PURE UUID: 59d8a260-8dba-435a-8c5a-4b56e94d2396

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Date deposited: 09 Nov 2018 17:30
Last modified: 21 Nov 2021 14:19

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Contributors

Author: Nataliia Gavryliuk
Author: Atul Bhaskar

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