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Response localization in disordered structures governed by the Sturm-Liouville differential equation. (Review)

Response localization in disordered structures governed by the Sturm-Liouville differential equation. (Review)
Response localization in disordered structures governed by the Sturm-Liouville differential equation. (Review)
The review is dedicated to the relatively new problem in structural engineering: localization of the response by structural irregularities. This review is aimed to outline all relevant discoveries in the response localization in mechanical problems (vibration, buckling) from the perspective of the common mathematical representation through Sturm-Liouville problem. Two possible approaches to analyze the influence of the disorder are discussed: exact dynamic stiffness formulation of the mistuned structure and the perturbation of the eigen solution of the tuned structure. Both approaches shown to lead to the same localization phenomena end exponential decay of the eigenvector from the source of disorder. In the section dedicated to the buckling mode localization the approach to analyze localization of the randomly disordered multi-span beam based on the Furstenberg’s theorem in presented. The examples of the localization phenomena in the real engineering structures are given.
Response localization, Wave propagation, Buckling, Irregularities, Disorder, REVIEW
2305-9001
123-132
Iakovliev, Andrii
8f2242a2-fb0e-4603-aed8-f17331846df7
Iakovliev, Andrii
8f2242a2-fb0e-4603-aed8-f17331846df7

Iakovliev, Andrii (2015) Response localization in disordered structures governed by the Sturm-Liouville differential equation. (Review). Journal of Mechanical Engineering NTUU Kyiv Polytechnic Institute, (74), 123-132. (doi:10.20535/2305-9001.2015.74.51048).

Record type: Review

Abstract

The review is dedicated to the relatively new problem in structural engineering: localization of the response by structural irregularities. This review is aimed to outline all relevant discoveries in the response localization in mechanical problems (vibration, buckling) from the perspective of the common mathematical representation through Sturm-Liouville problem. Two possible approaches to analyze the influence of the disorder are discussed: exact dynamic stiffness formulation of the mistuned structure and the perturbation of the eigen solution of the tuned structure. Both approaches shown to lead to the same localization phenomena end exponential decay of the eigenvector from the source of disorder. In the section dedicated to the buckling mode localization the approach to analyze localization of the randomly disordered multi-span beam based on the Furstenberg’s theorem in presented. The examples of the localization phenomena in the real engineering structures are given.

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More information

e-pub ahead of print date: 3 November 2015
Published date: 2015
Keywords: Response localization, Wave propagation, Buckling, Irregularities, Disorder, REVIEW

Identifiers

Local EPrints ID: 423050
URI: https://eprints.soton.ac.uk/id/eprint/423050
ISSN: 2305-9001
PURE UUID: fe71e304-0551-4e7c-825b-e7e442e8a239
ORCID for Andrii Iakovliev: ORCID iD orcid.org/0000-0003-4031-0073

Catalogue record

Date deposited: 13 Aug 2018 16:30
Last modified: 14 Mar 2019 01:28

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