Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 17, pp. 1-24.

Title: Signorini's problem for the Bresse beam model with localized Kelvin-Voigt dissipation

Authors: Jaime E. Munoz Rivera (National Laboratory for Sci. Computation, Rio de Janeiro, Brazil)
         Carlos A. da Costa Baldez (Federal Univ. of Para, Brazil)
         Sebastiao M. S. Cordeiro (Federal Univ. of Para, Brazil)

Abstract: 
We prove the existence of a global solution to Signorini's problem for the localized
viscoelastic Bresse beam model (circular arc) with continuous and discontinuous
constitutive laws. We show that when the constitutive law is continuous, the
solution decays exponentially to zero, and when the constitutive law is
discontinuous the solution decays only polynomially to zero.
The method we use for proving our result is different the others already used
in Signorini's problem and is based on approximations through a hybrid model.
Also, we present some numerical results using discrete approximations in time
and space, based on the finite element method on the spatial variable and the
implicit Newmark method to the discretized the temporal variable.

Submitted October 12, 2023. Published February 13, 2024.
Math Subject Classifications: 74H45, 74H20, 74H15, 93D20, 74K10, 74M15.
Key Words: Bresse beams; dynamic vibrations; contact problem;
    localized dissipation; asymptotic behavior; numerical experiment.