Vibration mitigation of a nonlinear rotor system with linear and nonlinear vibration absorbers

Abstract 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 using 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 parameters 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 obtained 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 respectively 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.

[1]  S. Chandraker,et al.  Dynamic study of viscoelastic rotor: Modal analysis of higher order model considering various asymmetries , 2017 .

[2]  幸男 石田,et al.  動吸振器を用いた非線形回転軸系の制振(機械力学,計測,自動制御) , 2002 .

[3]  Andrew Y. T. Leung,et al.  BIFURCATION BEHAVIOR OF A ROTOR SUPPORTED BY ACTIVE MAGNETIC BEARINGS , 2000 .

[4]  Majid Shahgholi,et al.  Vibration mitigation of a rotating beam under external periodic force using a nonlinear energy sink (NES) , 2017 .

[5]  N. Saeed,et al.  Nonlinear PD-controller to suppress the nonlinear oscillations of horizontally supported Jeffcott-rotor system , 2016 .

[6]  Oleg Gendelman,et al.  Robustness of nonlinear targeted energy transfer in coupled oscillators to changes of initial conditions , 2007 .

[7]  George Nikolakopoulos,et al.  A state-of-the-art review of structural control systems , 2015 .

[8]  W. D. Mark,et al.  Random Vibration in Mechanical Systems , 1963 .

[9]  K. M. Hsiao,et al.  VIBRATION ANALYSIS OF A ROTATING TIMOSHENKO BEAM , 2001 .

[10]  J. Ormondroyd.  Theory of the Dynamic Vibration Absorber , 1928 .

[11]  Alexander F. Vakakis,et al.  Steady State Passive Nonlinear Energy Pumping in Coupled Oscillators: Theoretical and Experimental Results , 2003 .

[12]  Tsuyoshi Inoue,et al.  Nonlinear normal modes and primary resonance of horizontally supported Jeffcott rotor , 2011 .

[13]  Mostafa Ghayour,et al.  Nonlinear dynamic analysis and experimental verification of a magnetically supported flexible rotor system with auxiliary bearings , 2018 .

[14]  Majid Shahgholi,et al.  Vibration attenuation of a rotor supported by journal bearings with nonlinear suspensions under mass eccentricity force using nonlinear energy sink , 2015 .

[15]  Pierre-Alain Masserey,et al.  Eddy Current Damper for Turbine Blading: Electromagnetic Finite Element Analysis and Measurement Results , 2012 .

[16]  Majid Shahgholi,et al.  Free vibration analysis of a nonlinear slender rotating shaft with simply support conditions , 2014 .

[17]  Walter Sextro,et al.  Spatial Dynamics of Tuned and Mistuned Bladed Disks with Cylindrical and Wedge-Shaped Friction Dampers , 2003 .

[18]  Alexander F. Vakakis,et al.  Vibration reduction in unbalanced hollow rotor systems with nonlinear energy sinks , 2015 .

[19]  Y. Ishida.  New Passive Control Methods for Reducing Vibrations of Rotors: Discontinuous Spring Characteristics and Ball Balancers , 2011 .

[20]  Majid Shahgholi,et al.  Lateral vibration attenuation of a rotor under mass eccentricity force using non-linear energy sink , 2014 .

[21]  Morteza Dardel,et al.  Steady state dynamics and robustness of a harmonically excited essentially nonlinear oscillator coupled with a two-DOF nonlinear energy sink , 2015 .

[22]  Christophe Pierre,et al.  The dynamic response of tuned impact absorbers for rotating flexible structures , 2006 .

[23]  Steven W. Shaw,et al.  Vibration absorbers for a rotating flexible structure with cyclic symmetry: nonlinear path design , 2010 .

[24]  Stephan Rinderknecht,et al.  Unbalance and resonance elimination with active bearings on a Jeffcott Rotor , 2017 .

[25]  N. Saeed,et al.  On the nonlinear oscillations of a horizontally supported Jeffcott rotor with a nonlinear restoring force , 2017 .

[26]  D. M. McFarland,et al.  Passive non-linear targeted energy transfer and its applications to vibration absorption: A review , 2008 .

[27]  D. M. McFarland,et al.  Experimental Targeted Energy Transfer to a Rotary Nonlinear Energy Sink , 2010 .

[28]  Ali H. Nayfeh,et al.  Steady-State dynamics of a linear structure weakly coupled to an essentially nonlinear oscillator , 2006 .

[29]  Majid Shahgholi,et al.  Nonlinear vibration analysis of a spinning shaft with multi-disks , 2015 .

[30]  Malte Krack,et al.  Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and its Application to Bladed Disks With Shroud Contact , 2013 .