Decay in thermoelastic Timoshenko systems with suspenders and partial Kelvin-Voigt damping

This work is focused on analyzing the stability of a thermoelastic Timoshenko system with suspenders and partial Kelvin–Voigt damping. The thermoelastic effect is governed by Cattaneo's law of heat propagation, this thermal dissipation is known to correct the infinite propagation of heat flow inherent in the application of the Fourier law of heat propagation, however, it is not without challenges when used in modeling the effect of temperature changes and how it affects the stability of a Timoshenko system. In most cases, stabilizing a Timoshenko system modeled with Cattaneo's law would require obtaining some stability criteria depending on the parameters of the Timoshenko model, unfortunately, in the real sense of it, these criteria are not generally obtainable from the physical standpoint, other than theoretically. The current work establishes an exponential decay rate for the associated energy functional without any stability criterion, i.e. independent of the physical parameters of the Timoshenko system. We also improved on a recent stability result of Mukiawa et al. [Thermal Timoshenko beam system with suspenders and Kelvin–Voigt damping. Front Appl Math Stat. 2023;9:1153071. doi: 10.3389/fams.2023.1153071].