Singular limits and dynamics for the abstract timoshenko system

We investigate dynamics of a class of abstract Timoshenko model with damping and source terms. We obtain a abstract Kirchhoff model as a singular limit of the abstract Timoshenko model when a certain coupling parameter a tends to infinity. Smooth global attractors with finite fractal dimension and exponential attractors are obtained using the recent quasi-stability theory. We conclude the work comparing the abstract Timoshenko model with abstract Kirchhoff model, in the sense of the upper-semicontinuity of their attractors as a tends to infinite.