Truncated Bresse-Timoshenko beam with fractional Laplacian damping

Abstract

This article focuses on a Timoshenko beam model introduced by Elishakoff. This model is free of the second frequency spectrum and solves the paradox of equal wave speeds, related to Timoshenko’s model. Damping created by a fractional Laplacian is considered, which includes internal damping, Kelvin-Voigt damping, and intermediate damping. Exponential stability is shown without requiring any relationship between the system coefficients