The dynamic response of a parametrically excited cantilever beam with a pendulum is theoretically and experimentally presented. The equation of motion and the associated boundary conditions are derived considering the static friction of the rotating motion at the supporting point (pivot) of the pendulum. It is theoretically shown that the static friction at the pivot of the pendulum plays a dominant role in the suppression of parametric resonance. The boundary conditions are different between two states in which the motion of the pendulum is either trapped by the static friction or it is not. Because of this variation of the boundary conditions depending on the pendulum motion, the natural frequencies of the system are automatically and passively changed and the bifurcation set for the parametric resonance is also shifted, so that parametric resonance does not occur. Experimental results also verify the effect of the pendulum on the suppression of parametric resonance in the cantilever beam.
Suppression of Parametric Resonance in Cantilever Beam With a Pendulum (Effect of Static Friction at the Supporting Point of the Pendulum)
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 2000; revised, February 2003; Associate Technical Editor: A. F. Vakakis.
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Yabuno, H., Murakami, T., Kawazoe, J., and Aoshima, N. (February 26, 2004). "Suppression of Parametric Resonance in Cantilever Beam With a Pendulum (Effect of Static Friction at the Supporting Point of the Pendulum) ." ASME. J. Vib. Acoust. January 2004; 126(1): 149–162. https://doi.org/10.1115/1.1596554
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