Periodic Responses of a Structure with 3:1 Internal Resonance

AD Shaw (Swansea University), TL Hill, SA Neild (University of Bristol) & MI Friswell (Swansea University)

Mechanical Systems and Signal Processing, Vol. 81, December 2016, pp. 19-34


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.

Paper Availability

This material has been published in the Mechanical Systems and Signal Processing, Vol. 81, December 2016, pp. 19-34, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier.

Link to paper using doi: 10.1016/j.ymssp.2016.03.008

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