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Shock and Vibration
Volume 2017 (2017), Article ID 5652023, 12 pages
Research Article

Analysis of the Viscoelastic Sphere Impact against a Viscoelastic Uflyand-Mindlin Plate considering the Extension of Its Middle Surface

Research Center for Wave Dynamics of Solids and Structures, Voronezh State Technical University, 20 Letija Oktjabrja Str. 84, Voronezh 394006, Russia

Correspondence should be addressed to Marina V. Shitikova; ur.liamv@avokitihs

Received 7 August 2016; Accepted 13 November 2016; Published 17 January 2017

Academic Editor: Ivo Caliò

Copyright © 2017 Yury A. Rossikhin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the present paper, the problem on impact of a viscoelastic sphere against a viscoelastic plate is considered with due account for the extension of plate’s middle surface and local bearing of sphere and plate’s materials via the Hertz theory. The standard linear solid models with conventional derivatives and with fractional-order derivatives are used as viscoelastic models, respectively, outside and within the contact domain. As a result of impact, transient waves (surfaces of strong discontinuity) are generated in the plate, behind the wave fronts of which up to the boundaries of the contact domain the solution is constructed in terms of one-term ray expansions due to short-time duration of the impact process. The motion of the contact zone occurs under the action of extension forces acting in the plate’s middle surface, transverse force, and the Hertzian contact force. The suggested approach allows one to find the time-dependence of the impactor’s indentation into the target and the Hertzian contact force.