Theoretical-experimental investigation of a three-degree-of-freedom structure

T. A. Nayfeh, A. H. Nayfeh, D. T. Mook

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


A theoretical-experimental investigation is conducted into the response of a three-degree-of-freedom structure having an autoparametric combination resonance of the additive type to a primary resonance of the higher mode. The structure consists of two light-weight beams and three concentrated masses arranged in a T-shape. The theoretically predicted natural frequencies are in good agreement with those obtained experimentally. The method of multiple scales is used to determine six first-order differential equations describing the modulation of the amplitudes and phases of the three modes with nonlinearity, damping, and resonances. Some of the predicted nonlinear phenomena include the saturation phenomenon, coexistence of stable solutions, jumps, and periodic, two-period quasiperiodic, and phase-locked or synchronized motions. The experiment confirms these predictions and shows other phenomena that are not yet explained by the theory.

Original languageEnglish (US)
Pages (from-to)2014-2025
Number of pages12
JournalCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
Issue numberpt 4
StatePublished - Jan 1 1990
Event31st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Part 3 (of 4): Structural Dynamics I - Long Beach, CA, USA
Duration: Apr 2 1990Apr 4 1990

ASJC Scopus subject areas

  • Architecture
  • Materials Science(all)
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering


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