Abstract

Nonlinear vibrations in an axially driven limber cantilever beam are studied experimentally to determine whether the observed aperiodic motions are chaotic, and to find the attractor dimension. Using the method of delays and time series calculations, the largest Lyapunov exponent is found to be positive, indicating that the aperiodic motions are chaotic. The correlation and embedding dimensions are computed; a phase space dimension in the range of 5–7 is found for the chaotic attractor. The system is also studied analytically, using a truncated Galerkin reduction of the planar equation of motion. It is found that this analytical approach does model the near-harmonic periodic motions of this system; however, the chaotic motions and chaotic transitions are not predicted. The model does exhibit interesting chaotic responses for non-physical values of the driving parameters.

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