Mechanism and Machine Theory 128 (2018) 586–615 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory Research paper Vibration mitigation of a nonlinear rotor system with linear and nonlinear vibration absorbers Javad Taghipour, Morteza Dardel ∗ , Mohammad Hadi Pashaei Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Shariati Street, 47148-71167 Babol, Mazandaran, Iran a r t i c l e i n f o Article history: Received 6 June 2018 Revised 27 June 2018 Accepted 2 July 2018 Keywords: Jeffcott rotor Vibration absorbers Tuned mass damper Nonlinear energy sink Complex averaging Bifurcation a b s t r a c t Steady state dynamics of a horizontally supported Jeffcott rotor system under nonlinear restoring forces has been studied in this work. Vibration reduction of the rotor system us- ing linear tuned mass dampers (TMD), nonlinear energy sinks (NES), and combined energy sinks (TMD-NES) was studied. In addition, the analysis on the effects of different parame- ters on the dynamics of the rotor system has been conducted. In this study, semi-analytical modified complex averaging technique (MCXA), numerical arc-length continuation method, and ODE integration method have been used to solve the governing equations. The ob- tained results showed, all three types of absorbers including TMD, NES, and combined TMD-NES sufficiently good performance in vibration reduction of primary rotor system. In a closer view, it shows that TMD-NES, TMD, and NES have respectively better performance in vibration reduction. On the other hand, combined TMD-NES, NES, and TMD give re- spectively broader frequency range of stability. Finally, it’s concluded that in spite of good efficiency in vibration reduction for the design condition, all types of absorbers should be modified to be more robust against changes in parameters of primary system. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction Rotor systems such as various types of turbines, bladed discs, fans, helicopters, and rotating shafts, are of the most applicable systems in the modern world. Undesired vibrations and chaotic dynamics of such systems may cause fatigue, in- stability, damages and lots of destructions. Therefore, vibration analysis and control in such systems are of high importance. Numerous studies have been conducted to analyze different types of rotor systems [1–7]. Shahgholi et al. [1] studied the free vibration of a nonlinear slender rotating shaft with simply support conditions. Considering the rotary inertia and gyroscopic effect, they concluded that for natural vibrations of a slender rotating shaft, backward and forward modes are in- volved. In 2015, Shahgholi et al. [2] studied the stability of a rotor system close to the major critical speeds, in which several discs were mounted on a simply supported nonlinear spinning shaft. They showed that for the higher and lower rotational speeds there are direct and inverse relationships between the backward frequency and the number of discs, respectively. They also revealed that with respect to shaft with small number of discs, by increasing the number of discs bifurcations occur in the lower speeds. In 2001, Lin and Hsiao [3] studied the linear vibration of rotating Timoshenko beam. For this purpose, they considered all inertia effect and coupling between extensional and flexural deformations. The effect of Corio- lis force was also considered in their study. They proposed a method based on the power series solution to solve the natural ∗ Corresponding author. E-mail address: Iran.dardel@nit.ac.ir (M. Dardel). https://doi.org/10.1016/j.mechmachtheory.2018.07.001 0094-114X/© 2018 Elsevier Ltd. All rights reserved.