Asymptotic Behavior of Rao–Nakra Sandwich Beam with Nonlinear Localized Damping and Source Terms

This paper is concerned with a semilinear Rao–Nakra sandwich beam under the action of three nonlinear localized frictional damping terms in which the core viscoelastic layer is constrained by the pure elasticity or piezoelectric outer layers. The main goal is to prove its asymptotic behavior by applying minimal amount of support to the damping. We firstly prove that the system is global well-posedness by the theory of monotone operators. For asymptotic behavior of solutions, we obtain uniform decay rate results of the system and the energy decay rates are determined by a nonlinear first-order ODE. The existence of a smooth global attractor with finite fractal dimension and generalized exponential attractors are finally obtained.