Exponential stability of a laminated beam system with thermoelasticity of type III and distributed delay

Abstract

In this work, we consider a one-dimensional laminated Timoshenko beam system with thermoelasticity of type III and distributed delay. Our concern is to investigate the exponential stability of the vibrations in the system without structural damping. By exploiting the perturbed energy method with appropriate assumptions on the delay feedback and speeds of wave propagation, we establish that the unique dissipation through the thermal effect is sufficient for exponential decay of the solution even in the presence of distributed delay.

Mathematics Subject Classification (2020):

• 35B40
• 35L56
• 74F05
• 93D15
• 93D23

Key words:

• Laminated beam
• thermoelasticity of type III
• distributed delay
• exponential decay