A contribution for nonlinear structural dynamics characterization of cantilever beams - Barros, Everaldo de; Mathias, Mauro Hugo [UNESP] (My University, 2005)
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.
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