Abstract
This investigation was concerned with the elastic impact of spheres on thin shallow spherical shells. A non-linear integro-differential equation of the impact process was developed on the basis of Reissner's approximate theory for transverse vibrations of shallow shells and the quasistatic Hertzian impact theory. This equation was numerically integrated and its main results were experimentally verified. Special attention was given to the apparently new observations that the rebound height of a sphere dropped onto a given shell has a minimum value for a critical size of the sphere, and that the contact time differs substantially for sphere sizes greater or less than this critical value.
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