The Effect of Viscoelasticity on the Vibration of a Rotor

Abstract

This paper analyzes the dynamics of a simple rotor mounted on a shaft constructed from a viscoelastic material. The equations are solved using a perturbation technique that is valid whenever viscoelastic time constants are much larger than elastic time constants. Regions of stable and unstable motion are discovered analytically. Several time histories for the rotor motion are presented.

Coupled bending torsional vibrations of viscoelastic rotors with fractional damper

“…In the absence of torsional effect, that is, φ=trueφ˙=trueφ¨=0, equations (18) to (20) are similar to the one obtained in equation (4) of (Hendricks, 1986), which was employed to analyze the dynamics of a rotor constructed from a viscoelastic material.…”

“…A variety of models exist in the literature to study the viscoelastic behavior especially in rotors (Ganguly et al, 2016, 2018; Hendricks, 1986; Roy and Chandraker, 2018), viscoelastically supported stator experiencing rub, or in non-contacting rotor-bearing systems through the use of linear spring and viscous damper components (Patel et al, 2012; Smyth et al, 2016). Furthermore, the fractional calculus has been used by a number of studies for analyzing viscoelastically damped structures (Abu-Mallouh et al, 2012; Agrawal, 2004; Bagley and Torvik, 1983; Demir et al, 2012; Di Lorenzo et al, 2014; Liang and Tang, 2007; Ray et al, 2005; Sakakibara, 1997; Spanos and Malara, 2014).…”

“…Here, an approach similar to that adopted in (Gosiewski, 2008) is implemented to derive a general formulation/solution for three-mode rotor model (Jeffcott’s model). Two distinct advances with respect to the earlier works (Gosiewski, 2008; Hendricks, 1986; Kliem, 1987) are as follows: the present model incorporates complex interactions between the viscoelastic supports, the material viscoelasticity, lateral-torsional coupling, and the unbalance effect; and a new perspective on the instability in the presence of the viscoelasticity effect is captured using a fractional-calculus representation. This increases the complexity of the modeling drastically with respect to the earlier work.…”

Asymptotic analysis of the forced vibrations of a one-disc rotor on a non-linear flexible base

“…Non-stationary vibrations of the rotor with limited power supply are considered by Iwatsubo et al [7]. The destabilizing action of viscous damping on the dynamics of a rotor with different elastic properties in two orthogonal directions is analysed by Hendricks [8]. Kim and Noah [9] investigated subharmonic vibrations of the Jeffcott rotor taking into account a clearance in a bearing.…”