A State Space Viscoelastic Shaft Finite Element for Analysis of Rotors

The present work proposes a new shaft element for viscoelastic rotors in a spinning frame. The Maxwell-Wiechert viscoelastic material model which has one elastic branch and several parallel Maxwell branches of elastic and viscous elements in series is considered here. This model considers additional internal or damping variables between elastic and viscous elements. Here, the stress depends not only on the elastic strain and elastic strain rate but also on additional strains and their rates. In the present work, it is assumed that these additional strains can be derived from continuous fictitious displacement variables in the same way as the elastic strains are derived from the actual displacement variables. These continuous fictitious displacements in turn are interpolated from their nodal values using the conventional beam shape functions. Therefore, in addition to the standard degrees of freedom, extra degrees of freedom are defined at the nodes.