Dynamics of an exponentially damped solid rod: Analytic solution and finite element formulations

This paper presents the analytic solution together with two finite element formulations to obtain the dynamic response of an exponentially damped solid rod. The analysis is carried out in time domain, the material being modeled by the standard linear viscoelastic solid model. On the one hand, the analytic solution is reached by means of modal superposition by two different ways: with and without internal variables. On the other hand, two different finite element formulations are proposed: the first one is conceived for direct integration methods, and the other one is developed to apply modal superposition. The interest of modal superposition method lies on investigating the influence of non-viscous modes.

► The response of an exponentially damped rod is presented.
► The analytic solution is reached using and without using internal variables.
► Two finite element formulations are presented.
► One for direct integration methods, and the other to apply modal superposition.
► The influence of non-viscous modes is put into evidence.