Asymptotic behavior of laminated beams without rotational inertia

Abstract In this work, we propose and analyze a model for laminated beams that accounts for shear deformation while neglecting the effects of rotational inertia, serving as an analogue to the shear model for homogeneous beams. The proposed system consists of three coupled partial differential equations governing the transverse displacement, the effective rotation, and an internal variable associated with interfacial sliding. We first establish the well-posedness of the problem using the Faedo–Galerkin method. Then, we investigate the asymptotic behavior of the solution under two distinct damping configurations: one with dissipation in both the internal and rotational variables, and another with dissipation only in the transverse displacement. In the first case, we show that the system is not exponentially stable, and subsequently prove a polynomial decay with the optimal rate. In the second case, we prove exponential stability without imposing additional constraints on the physical coefficients. The results highlight the decisive role of the location of dissipative mechanisms in determining the stability of laminated beams without rotational inertia.