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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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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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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 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.
Keywords: Internal resonance; Vibration testing; Normal formIsola
Start Page: 19
End Page: 34