Membrane Spin Up in a Normal Gravity Field: Experiments and Simulations

Abstract

Finite element simulations and experimental observations of the spin up in vacuum of a thin membrane loaded by gravity are presented. The numerical techniques take into account the run time of each simulation and energy convergence; it is shown that accurate results can be obtained quite quickly in a rotating reference frame, and that including stiffness-proportional material damping helps convergence of the integration. It is also found that a very fine finite element mesh around the hub of the membrane is required to obtain consistent results. The experimental setup allows spinning of the membrane in a vacuum box; a measurement technique that uses stereo Digital Image Correlation is presented. A comparison between experiments and simulations using characteristic parameters of the shape of a membrane, i.e. the number of rotational symmetric waves, the average deflection, and the elastic bending strain energy of the membrane, shows good agreement between experiments and simulations.