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Machine Theory
Mechanism and Machine Theory 43 (2008) 1376–1384
ate/mechmt
Internal damping in rotating shafts
F. Vatta, A. Vigliani *
Dipartimento di anica, ico di Torino, Duca degli Abruzzi, 24, 10129 Torino, Italy
Received 21 February 2007; received in revised form 13 November 2007; accepted 22 December 2007
Available online 8 February 2008
Abstract
This paper analyses the influence of internal damping on the dynamic behaviour of rotating shafts. The problem is faced
considering the presence of nonlinearities introduced in the restoring elastic forces by the pression and exten-
sion of the shaft fibres; these forces show ponent that can oppose or drive the shaft whirl motion.
The analytical solutions obtained allow to describe the transient motion of the shaft and to evaluate the stability limit,
whose value slightly differs from the classical one determined with linear approaches.
Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Internal damping; Rotor dynamics; Nonlinear forces
1. Introduction
The term ‘‘internal damping” monly adopted regarding both the elastic hysteresis of materials and
the shaft fibre shear inside the hub [8,6]. When a rotating shaft undergoes a perturbation, consisting in dis-
placement and velocity variations of a point belonging to the shaft axis with respect to dynamic equilibrium