Non-local stiffness and damping models for shear-deformable beams

This paper presents the dynamics of a non-local Timoshenko beam. The key assumption involves
modeling non-local effects as long-range volume forces and moments mutually exerted by non-adjacent
beam segments, that contribute to the equilibrium of any beam segment along with the classical local
stress resultants. Elastic and viscous long-range volume forces/moments are endowed in the model. They
are built as linearly depending on the product of the volumes of the interacting beam segments and on
generalized measures of their relative motion, based on the pure deformation modes of the beam.
Attenuation functions governing the space decay of the non-local effects are introduced. Numerical results
are presented for a variety of non-local parameters.