Uniform stability for laminated beams with time-dependent boundary conditions

In this paper we consider a laminated beam model. This structure is given by two identical uniform layers on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. In the presence of nonlinear boundary controls modulated by time-dependent coefficients, we use the multiplier method and overcome the difficulty of finding suitable multipliers to establish a uniform stability result. This result provides an explicit formula for the energy decay rates without imposing any conditions on the coefficients of the system which is more meaningful and realistic from the physical point of view. Our result improves the earlier related results in the literature.

Automated summary

This paper investigates a laminated beam model, where two identical uniform layers are bonded together with a small thickness adhesive, resulting in interfacial slip. By considering nonlinear boundary controls and using the multiplier method, a uniform stability result is established without imposing any conditions on the coefficients of the system, providing an explicit formula for the energy decay rates.