6533b86cfe1ef96bd12c823d
RESEARCH PRODUCT
Exact non-Hookean scaling of cylindrically bent elastic sheets and the large-amplitude pendulum
Vyacheslavs Kashcheyevssubject
PhysicsPendulumGeneral Physics and AstronomyClassical Physics (physics.class-ph)FOS: Physical sciencesPhysics - Classical PhysicsPopular Physics (physics.pop-ph)Physics - Popular PhysicsCritical valueGravitationNonlinear systemAmplitudeClassical mechanicsSpring (device)CylinderScalingdescription
A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence on the interplate distance [Siber and Buljan, arXiv:1007.4699 (2010)]. The phenomenon has been used as a basis for an experimental problem at the 41st International Physics Olympiad. We show that the corresponding variational problem for the equilibrium energy of the deformed cylinder is equivalent to a minimum action description of a simple gravitational pendulum with an amplitude of 90 degrees. We use this analogy to show that the power-law of the force is exact for distances less than a critical value. An analytical solution for the elastic force is found and confirmed by measurements over a range of deformations covering both linear and non-Hookean behavior.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-08-27 |