The influence of damping on the asymptotic behavior of solution for laminated beam

Abstract

This paper dealt with a laminated beam system along with structural damping, past history, distributed delay, and in the presence of both temperatures and micro-temperatures effects. The damping terms left the system dissipative. Employing the semigroup approach, we established the existence and uniqueness of the solution. Additionally, with the help of convenient assumptions on the kernel, we demonstrated a general decay result for the solution of the considered system, with no constraints regarding the speeds of wave propagation. The main aim was to address how specific behaviors of the system were related to memory and delays. We aimed to investigate the joint impact of an infinite memory, distributed delay and micro-temperature effects on the system. We found a new relationship between the decay rate of solution and the growth of g at infinity. The objective was to find studies that use no- trivial results and their applications to relevant problems from mathematical physics.

Keywords

• laminated beam
• stability
• well-posedness
• micro-temperature effects
• structural damping
• lyapunov functions
• distributed delay
• past history
• dynamical systems