Elastodynamic Contact In Plate-like Bodies
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In this paper the dynamic problem of the frictionless normal low velocity impact of a rigid sphere against an elastic plate-like body is studied by assuming that the period of duration of the impact is much larger than the time employed by the elastic waves in traversing the plate after the first impact, using a static contact law taking into account the thickness of the plate and a Hertzian pressure distribution between the sphere and the plate is adopted. A non-linear second order ordinary differential equation for the dynamical value of the indentation is obtained and, by using a perturbative technique, numerical solutions concerning the contact period, the maximum contact force and the maximum indentation in terms of the plate thickness are obtained. Numerical investigations show how the time of collision decreases with the increasing of the thickness-to plate radius ratio, the maximum indentation decreases and the maximum contact force increases. All these values approach Hertz’s values when the plate thickness increases. It is remarked that the solution presented here is valid only when the contact area radius is \“small” in comparison to the plate thickness; if this assumption is not satisfied, the contact pressure distribution deviates significantly from the Hertzian prediction. Keywords: contact mechanics, dynamical impact, elasticity theory, elastic plate. 1 Introduction In this paper the dynamic problem of the frictionless normal low velocity impact of a rigid sphere against an elastic plate-like body is studied. In a dynamical framework an impact law taking into account the period load frequency and the thickness of the plate was obtained in ; nevertheless, if the period of duration of the impact is assumed much larger than the time employed by the elastic
contact mechanics, dynamical impact, elasticity theory, elastic plate.