Polynomial stability of the Bresse beam with local thermoelastic damping and viscous dissipation

In this study, we investigate the polynomial stabilization of a Bresse beam transmission problem in which thermoelastic damping is locally applied to the shear force and complemented by viscous damping on both shear and longitudinal motions. The thermoelastic component of the beam, which is subject to damping, exerts a stabilizing influence on the elastic portion through the transmission of damping effects. Leveraging an extended result derived from the Weyl theorem, we establish the non-exponential stability of the system. Furthermore, by employing a frequency domain method, we demonstrate the polynomial stability of the Bresse beam system. This research provides valuable insights into the complex interplay between thermal and elastic behaviors in Bresse beams, contributing to a deeper understanding of their dynamic stability characteristics.