Long-time dynamics of laminated beams with nonlinear localized damping and source terms

This paper is concerned with the long-time dynamics of the model of a laminated Timoshenko beam, which is a structure given by two-layered beams with structural damping as a result of an interfacial slip, with nonlinear localized damping mechanisms placed on an arbitrarily small support. We prove that the system admits a global attractor which is characterized as an unstable manifold of the set of stationary solutions. The regularity and finite fractal dimension of the global attractor is also proved. Finally, we obtain the existence of a generalized exponential attractor. All results are proved without any restrictions on the coefficients and the assumption of equal wave speed propagation.