Reinvestigation of the behavior of viscoelastic damping

Abstract

The Kelvin–Voigt and Zener viscoelasticity models have been studied using a stressed uniform bar. The presented results show that since a classic single element model and a real structure are governed by a first-order ordinary differential equation and a second/third-order partial differential equation, respectively, an ideal single element model will behave differently from a structure when acceleration has to be taken into account. When for a Zener viscoelasticity holds ${\tau_{\varepsilon} < \tau_{\sigma}}$ , then it may cause no a creep relaxation due to a positive real part of an eigenvalue in vibration that may become unstable. This suggests that the Zener model is valid for a real material when, and only when, ${\tau_{\varepsilon} \geq \tau_{\sigma}}$ . It has been found that the formulations of calculating Q ⁻¹ parameters developed in literature from a single element model may need to be improved and that the initial response obtained from a classic single element model relaxes far more quickly than that of a stressed bar.