On damping effects in Timoshenko beams

Abstract

In this paper, the dynamic response of a Timoshenko beam with distributed internal viscous damping (DIVD) is analyzed with the aim to ascertain their relative effects on the whole range of beam slenderness. With respect to some previous and quite recent works, some further and fundamental generalizations are therefore introduced. First, the decoupling of shear and bending damping mechanisms, with or without the presence of the external classical viscous contribution. This splitting allows the outlining of the relevant influences on the dynamic response associated to any singular damping mechanism and the evaluation of the modal critical damping. As a second contemporary step, an explicit dependency is set upon the shear slenderness of the beam model, allowing to study the dependence of each single damping mechanism upon the relevant kinematic model, spanning from truly Bernoulli's behavior to mainly Shear controlled responses. According to the selected damping model, the dynamic behavior automatically selects the characteristics of kinematical response (relative levels of shear and bending contributions) depending of the minimization of the total internal energy (i.e. elastic energy and dissipation). In the folds of this study, the problem of optimal piece-wise constant distribution of DIVD is finally also addressed, firstly showing that is possible to find non-trivial and interesting solutions.