Periodic responses of a structure with 3:1 internal resonance

Shaw, Alexander; Hill, T.L.; Neild, S.A.; Friswell, Michael

doi:10.1016/j.ymssp.2016.03.008

Journal article 1286 views 153 downloads

Periodic responses of a structure with 3:1 internal resonance

Alexander Shaw

, T.L. Hill, S.A. Neild, Michael Friswell

Mechanical Systems and Signal Processing, Volume: 81, Pages: 19 - 34

Swansea University Authors: Alexander Shaw , Michael Friswell

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DOI (Published version): 10.1016/j.ymssp.2016.03.008

Abstract

This work presents a conceptually simple experiment consisting of a cantilever beam with a nonlinear spring at the tip. The configuration allows manipulation of the relative spacing between the modal frequencies of the underlying linear structure, and this permits the deliberate introduction of inte...

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Published in:	Mechanical Systems and Signal Processing
ISSN:	0888-3270
Published:	2016
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa26775
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first_indexed	2016-03-18T01:59:36Z
last_indexed	2023-01-11T13:58:52Z
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spelling	2022-11-15T16:18:39.4934275 v2 26775 2016-03-17 Periodic responses of a structure with 3:1 internal resonance 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2016-03-17 AERO This work presents a conceptually simple experiment consisting of a cantilever beam with a nonlinear spring at the tip. The configuration allows manipulation of the relative spacing between the modal frequencies of the underlying linear structure, and this permits the deliberate introduction of internal resonance. A 3:1 resonance is studied in detail; the response around the first mode shows a classic stiffening response, with the addition of more complex dynamic behaviour and an isola region. Quasiperiodic responses are also observed but in this work the focus remains on periodic responses. Predictions using Normal Form analysis and continuation methods show good agreement with experimental observations. The experiment provides valuable insight into frequency responses of nonlinear modal structures, and the implications of nonlinearity for vibration tests. Journal Article Mechanical Systems and Signal Processing 81 19 34 0888-3270 Internal resonance; Vibration testing; Normal formIsola 15 12 2016 2016-12-15 10.1016/j.ymssp.2016.03.008 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University RCUK 2022-11-15T16:18:39.4934275 2016-03-17T18:09:23.8812337 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Alexander Shaw 0000-0002-7521-827X 1 T.L. Hill 2 S.A. Neild 3 Michael Friswell 4 0026775-726201643318PM.pdf ShawPeriodic_responses_of_a_structure.pdf 2016-07-26T16:33:18.4700000 Output 1836859 application/pdf Version of Record true 2016-07-26T00:00:00.0000000 Open Access funded by Engineering and Physical Sciences Research Council Under a Creative Commons license true http://creativecommons.org/licenses/by/4.0/
title	Periodic responses of a structure with 3:1 internal resonance
spellingShingle	Periodic responses of a structure with 3:1 internal resonance Alexander Shaw Michael Friswell
title_short	Periodic responses of a structure with 3:1 internal resonance
title_full	Periodic responses of a structure with 3:1 internal resonance
title_fullStr	Periodic responses of a structure with 3:1 internal resonance
title_full_unstemmed	Periodic responses of a structure with 3:1 internal resonance
title_sort	Periodic responses of a structure with 3:1 internal resonance
author_id_str_mv	10cb5f545bc146fba9a542a1d85f2dea 5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv	10cb5f545bc146fba9a542a1d85f2dea_*_Alexander Shaw 5894777b8f9c6e64bde3568d68078d40_*_Michael Friswell
author	Alexander Shaw Michael Friswell
author2	Alexander Shaw T.L. Hill S.A. Neild Michael Friswell
format	Journal article
container_title	Mechanical Systems and Signal Processing
container_volume	81
container_start_page	19
publishDate	2016
institution	Swansea University
issn	0888-3270
doi_str_mv	10.1016/j.ymssp.2016.03.008
college_str	Faculty of Science and Engineering
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department_str	School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str	1
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description	This work presents a conceptually simple experiment consisting of a cantilever beam with a nonlinear spring at the tip. The configuration allows manipulation of the relative spacing between the modal frequencies of the underlying linear structure, and this permits the deliberate introduction of internal resonance. A 3:1 resonance is studied in detail; the response around the first mode shows a classic stiffening response, with the addition of more complex dynamic behaviour and an isola region. Quasiperiodic responses are also observed but in this work the focus remains on periodic responses. Predictions using Normal Form analysis and continuation methods show good agreement with experimental observations. The experiment provides valuable insight into frequency responses of nonlinear modal structures, and the implications of nonlinearity for vibration tests.
published_date	2016-12-15T03:32:14Z
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score	11.016235

Periodic responses of a structure with 3:1 internal resonance

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