Electron. J. Differential Equations, Vol. 2024 (2024), No. 17, pp. 1-24.

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

Jaime E. Munoz Rivera, Carlos A. da Costa Baldez, Sebastiao M. S. Cordeiro

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.
DOI: 10.58997/ejde.2024.17

Show me the PDF file (1023 KB), TEX file for this article.

Jaime E. Muñoz Rivera
National Laboratory for Scientific Computation
Petrópolis, Rio de Janeiro, Brazil
email: jemunozrivera@gmail.com
Carlos A. da Costa Baldez
Department of Mathematics
Federal University of Pará
Bragança, Pará, Brazil
email: baldez@ufpa.br
Sebastião M. S. Cordeiro
Department of Mathematics
Federal University of Pará
Abaetetuba, Pará, Brazil
email: sebastiao@ufpa.br

Return to the EJDE web page