Uniform stability for a semilinear laminated Timoshenko beams posed in inhomogeneous medium with localized nonlinear damping

Abstract This paper is mainly concerned with the stabilization of a semilinear laminated Timoshenko beams, posed in an inhomogeneous medium, under the actionof three nonlinear localized frictional damping terms. Such a problem consists of two identical layers of uniform thickness, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. The main objective is to prove the uniform decay rates for the energy of the considered problemby imposing minimal amount of support for the damping and with no restrictions around the non-constant coefficients. The proof of the desired result is based on some techniques of the Microlocal Analysis Theory.