Asymptotic behavior of solutions of a viscoelastic Shear beam model with no rotary inertia: General and optimal decay results

In this study, we consider a viscoelastic Shear beam model with no rotary inertia. Specifically, we study {equation presented} where the convolution memory function g belongs to a class of L¹ (0, ∞) functions that satisfies {equation presented} where ζ is a positive nonincreasing differentiable function and ϵ is an increasing and convex function near the origin. Using just this general assumptions on the behavior of g at infinity, we provide optimal and explicit general energy decay rates from which we recover the exponential and polynomial rates when ϵ (s)=s^p and p covers the full admissible range [ 1, 2). Given this degree of generality, our results improve some of earlier related results in the literature.