Periodic responses of a structure with 3:1 internal resonance

• Published in: Mechanical systems and signal processing 2016-12, Vol.81, p.19-34
• Main Authors: Shaw, A.D., Hill, T.L., Neild, S.A., Friswell, M.I.
• Format: Article
• Language: English
• Subjects: Cantilever beams; Continuation methods; Dynamic tests; Internal resonance; Isola; Mechanical systems; Nonlinear dynamics; Nonlinearity; Normal form; Signal processing; Stiffening; Vibration testing
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2016.03.008

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. •Experimental demonstration of 3:1 internal resonance in an easy to reproduce structure with transparent underlying physics.•Experimental demonstration of isolated region in frequency response.•Normal forms/backbone analysis of the free structure used to explain the rich dynamics seen.•Reasonable match with continuation analysis in AUTO; the revealed structure of bifurcations sheds further light on the response of the forced and damped system.