Chaos in a Harmonically Excited Elastic Beam

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Abstract
Numerical integration of the equations for the evolution of amplitudes of a harmonically forced simply supported elastic beam indicates that for certain values of the frequencies of excitation the response of the beam may be chaotically modulated. In an attempt to confirm the presence of chaos, the Lyapunov exponents have been calculated for two cases in which the broadening of the power spectra around the dominant peaks occurs. In both the cases one of the Lyapunov exponents is positive; this provides further evidence of chaos. The Lyapunov dimension of the attractors in these cases is estimated to be 2.09 and 2.11, respectively.

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