Periodic responses of a structure with 3:1 internal resonance

Alexander D Shaw, Tom L Hill, Simon A Neild, Michael I Friswell

Research output: Contribution to journalArticle (Academic Journal)peer-review

50 Citations (Scopus)
361 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)19-34
Number of pages16
JournalMechanical Systems and Signal Processing
Early online date31 Mar 2016
Publication statusPublished - 15 Dec 2016


  • Internal resonance
  • Vibration testing
  • Normal form
  • Isola


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