Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates

TL;DR

This paper proves the solvability of a dynamic contact problem with limited interpenetration for various viscoelastic plate models, showing convergence to Signorini contact solutions as interpenetration thickness diminishes.

Contribution

It establishes the existence of solutions for complex viscoelastic plate contact models and demonstrates convergence to classical contact solutions as interpenetration reduces.

Findings

Existence of solutions for multiple viscoelastic plate models.

Convergence of solutions to Signorini contact as interpenetration tends to zero.

Applicability to classical and singular memory viscoelasticity.

Abstract

The solvability of the rational contact with limited interpenetration of different kind of viscolastic plates is proved. The biharmonic plates, von K\'arm\'an plates, Reissner-Mindlin plates and full von K\'arm\'an systems are treated. The viscoelasticity can have the classical (``short memory'') form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of the Signorini contact is proved provided the thickness of the interpenetration tends to zero.