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Developable modes in vibrated thin plates.

Arezki Boudaoud1, Eugenio Hamm, Francisco Melo

  • 1Laboratoire de Physique Statistique, UMR 8550 du CNRS, Ecole Normale Supérieure, Universités Paris VI et Paris VII, 24 rue Lhomond, 75231 Paris Cedex 05, France.

Physical Review Letters
|February 1, 2008
PubMed
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Parametric excitation of a developable cone singularity leads to two bending modes: rolling and tilt. High-amplitude rolling modes cause continuous rotation and material displacement, akin to a moving carpet wrinkle.

Area of Science:

  • Solid Mechanics
  • Nonlinear Dynamics
  • Material Science

Background:

  • Investigates the complex behavior of developable cone singularities formed by circular sheets on rigid frames.
  • Focuses on the dynamic response under central forcing and sinusoidal excitation.

Purpose of the Study:

  • To analyze the normal modes and parametric excitation phenomena in a developable cone singularity.
  • To characterize the distinct rolling and tilt bending modes and their behavior under varying vibration amplitudes.

Main Methods:

  • Experimental setup involving a circular sheet supported by a rigid frame, subjected to central and sinusoidal forcing.
  • Observation and analysis of the resulting bending modes, specifically the rolling and tilt modes.

Main Results:

Related Experiment Videos

  • Identified two primary bending modes: rolling and tilt, which are parametrically excited by sinusoidal forcing.
  • Observed that sufficiently high amplitudes of the rolling mode lead to dramatic increases in amplitude.
  • Demonstrated that this leads to continuous rotation of the concave sector and material angular displacement.

Conclusions:

  • Developable cone singularities exhibit complex dynamic behaviors under external forcing.
  • Parametric excitation can induce significant shape transformations, including continuous rotation and material displacement.
  • The rolling mode's behavior at high amplitudes presents a novel dynamic phenomenon with potential analogies to macroscopic material behaviors.