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Periodic responses of a structure with 3:1 internal resonance

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

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

Swansea University Authors: Alexander Shaw Orcid Logo, Michael Friswell

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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa26775
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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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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
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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 2016-12-15T03:32:16Z
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score 10.927203