A contribution for nonlinear structural dynamics characterization of cantilever beams
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Abstract
Successful experiments in nonlinear vibrations have been carried out with cantilever beams under harmonic base excitation. A flexible slender cantilever has been chosen as a convenient structure to exhibit modal interactions, subharmonic, superharmonic and chaotic motions, and others interesting nonlinear phenomena. The tools employed to analyze the dynamics of the beam generally include frequency- and force-response curves. To produce force-response curves, one keeps the excitation frequency constant and slowly varies the excitation amplitude, on the other hand, to produce frequency-response curves, one keeps the excitation amplitude fixed and slowly varies the excitation frequency. However, keeping the excitation amplitude constant while varying the excitation frequency is a difficult task with an open-loop measurement system. In this paper, it is proposed a closed-loop monitor vibration system available with the electromagnetic shaker in order to keep the harmonic base excitation amplitude constant. This experimental setup constitutes a significant improvement to produce frequency-response curves and the advantages of this setup are evaluated in a case study. The beam is excited with a periodic base motion transverse to the axis of the beam near the third natural frequency. Modal interactions and two-period quasi-periodic motion are observed involving the first and the third modes. Frequency-response curves, phase space and Poincaré map are used to characterize the dynamics of the beam.
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Keywords
Base excitation, Base motion, Chaotic motions, Closed-loop, Electromagnetic shakers, Excitation amplitudes, Excitation frequency, Frequency-response curves, Measurement system, Modal interactions, Non-linear phenomena, Non-linear vibrations, Nonlinear structural dynamics, Phase spaces, Poincare, Quasi-periodic motion, Subharmonics, Super-harmonic, Vibration systems, Dynamics, Phase space methods, Structural dynamics, Cantilever beams
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English
Citation
International Congress on Noise Control Engineering 2005, INTERNOISE 2005, v. 3, p. 1950-1959.
