Dynamic stability of an elastic beam with visco-elastic translational and rotational supports

Purpose – The purpose of this paper is to show how to find the regions of dynamic instability of a beam axially loaded and visco-elastically constrained at its ends by Kelvin-Voigt translational and rotational units variously arranged according to different configurations, by using the equation of boundary frequencies. Design/methodology/approach – With respect to visco-elasticity the time variable is present as a parameter so that the above-mentioned exact approach is exploited to draw three-dimensional diagrams of the dynamic component of the periodic load and its frequency, varying with time and with the viscosity parameter m characterizing the restraints. Findings – For not rigidly constrained configurations a peculiar asymptotic tendency is recognizable in both cases. Research limitations/implications – The study allows for identifying the influence of visco-elastic restraints in the response of a beam under a dynamic axial load. Dynamic excitation occurs in several fields of mechanics: dynamic loads are encountered in structural systems subjected to seismic action, aircraft structures under the load of a turbulent flow and industrial machines whose components transmit time-dependant forces. Practical implications – Visco-elasticity accounts for possible vibration control solutions planned to improve the dynamic response of the rod; they can consist of layers of visco-elastic material within the body of the modelled element or local viscous instruments affecting the boundary conditions; the latter is the application this paper focuses on. Originality/value – With this paper a calculation procedure to get an exact solution for particular static configurations of the beam is followed in order to define the influence of visco-elastic restraints under a dynamic axial load; the responses are given in terms of boundary frequencies domains and are supposed to be useful to learn the behaviour in time and in dependence of the intrinsic viscosity of the restraints.