Torsional Vibration Reduction of a Rotor by Using Nonlinear Dual Dynamic Vibration Absorber

Document Type : Research Article

Authors

Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran

Abstract

Torsional vibrations in rotors can lead to fatigue failure and system instability, making effective vibration control critical for industrial applications. This study proposes a nonlinear dual dynamic vibration absorber to mitigate torsional vibrations in a rotor. The absorber consists of two symmetric sets, each comprising a mass, spring, and damper, seamlessly integrated onto the rotor disc for practical implementation. The key equations describing the system's behavior are derived using the Lagrangian method and, due to their nonlinearity, solved using the method of multiple scales. The influence of the absorbers' mass and distance ratios on the torsional vibration amplitude at resonance is investigated, revealing that equal mass and distance ratios optimize performance. Specifically, the absorber reduces the vibration amplitude at resonance from 0.03 radians to 0.5 milliradians. The effect of damping on vibration suppression is also analyzed, and a comparison between linear and nonlinear states demonstrates the superior efficacy of the nonlinear approach. Unlike conventional single or linear absorbers, this dual nonlinear design significantly enhances vibration reduction at resonance, offering improved rotor stability and durability for industrial systems.

Keywords

Main Subjects

References

[1] H. Frahm, Device for damping vibrations of bodies, in, Google Patents, 1911.
[2] J. Ormondroyd, J. Den Hartog, The theory of the dynamic vibration absorber, Journal of Fluids Engineering, 49(2) (1928).
[3] K. Iwanami, K. Seto, An optimum design method for the dual dynamic damper and its effectiveness, Bulletin of JSME, 27(231) (1984) 1965-1973.
[4] T. Asami, Optimal design of double-mass dynamic vibration absorbers arranged in series or in parallel, Journal of Vibration and Acoustics, 139(1) (2017) 011015.
[5] Y. Shen, H. Peng, X. Li, S. Yang, Analytically optimal parameters of dynamic vibration absorber with negative stiffness, Mechanical Systems and Signal Processing, 85 (2017) 193-203.
[6] M.M. Nazari, A. Rahi, Parameters optimization of a nonlinear dynamic absorber for a nonlinear system, Archive of Applied Mechanics, 93(8) (2023) 3243-3258.
[7] W.-B. Shangguan, X.-Y. Pan, Multi-mode and rubber-damped torsional vibration absorbers for engine crankshaft systems, International Journal of Vehicle Design, 47(1-4) (2008) 176-188.
[8] X.-T. Vu, D.-C. Nguyen, D.-D. Khong, V.-C. Tong, Closed-form solutions to the optimization of dynamic vibration absorber attached to multi-degrees-of-freedom damped linear systems under torsional excitation using the fixed-point theory, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 232(2) (2018) 237-252.
[9] V. Manchi, C. Sujatha, Torsional vibration reduction of rotating shafts for multiple orders using centrifugal double pendulum vibration absorber, Applied Acoustics, 174 (2021) 107768.
[10] Y. Cao, H. Yao, J. Dou, C. Wu, Torsional vibration suppression of rotor systems using a rubber-based nonlinear energy sink, Meccanica, 58(4) (2023) 565-585.
[11] B. Xiang, W. Wong, Electromagnetic vibration absorber for torsional vibration in high speed rotational machine, Mechanical Systems and Signal Processing, 140 (2020) 106639.
[12] D.-C. Nguyen, Determination of optimal parameters of the tuned mass damper to reduce the torsional vibration of the shaft by using the principle of minimum kinetic energy, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 233(2) (2019) 327-335.
[13] Y. Shen, Z. Xing, S. Yang, J. Sun, Parameters optimization for a novel dynamic vibration absorber, Mechanical Systems and Signal Processing, 133 (2019) 106282.
[14] X. Wang, B. Yang, H. Yu, Optimal design and experimental study of a multidynamic vibration absorber for multifrequency excitation, Journal of Vibration and Acoustics, 139(3) (2017) 031011.
[15] Y. Chang, J. Zhou, K. Wang, D. Xu, A quasi-zero-stiffness dynamic vibration absorber, Journal of sound and vibration, 494 (2021) 115859.
[16] Y. Cheung, W. Wong, Design of a non-traditional dynamic vibration absorber, The Journal of the Acoustical Society of America, 126(2) (2009) 564-567.
[17] D. Tchokogoué, M. Mu, B.F. Feeny, B.K. Geist, S.W. Shaw, The effects of gravity on the response of centrifugal pendulum vibration absorbers, Journal of Vibration and Acoustics, 143(6) (2021) 061011.
[18] M. Rao, C. Sujatha, Design of centrifugal pendulum vibration absorber to reduce the axial vibration of rotating shafts for multiple orders, SAE International Journal of Passenger Cars-Mechanical Systems, 13(06-13-02-0007) (2020) 81-105.
[19] K. Kecik, Assessment of energy harvesting and vibration mitigation of a pendulum dynamic absorber, Mechanical Systems and Signal Processing, 106 (2018) 198-209.
[20] A. El-Sayed, H. Bauomy, Vibration suppression of subharmonic resonance response using a nonlinear vibration absorber, Journal of Vibration and Acoustics, 137(2) (2015) 024503.
[21] S.W. Shaw, R. Bahadori, Tuning of centrifugal pendulum vibration absorbers operating in a fluid, Nonlinear Dynamics, 112(2) (2024) 741-755.
[22] T. Abu Seer, N. Vahdati, O. Shiryayev, Adaptive torsional tuned vibration absorber for rotary equipment, Vibration, 2(1) (2019) 116-134.
[23] R. Faal, B. Crawford, R. Sourki, A. Milani, Experimental, numerical and analytical investigation of the torsional vibration suppression of a shaft with multiple optimal undamped absorbers, Journal of Vibration Engineering & Technologies, 9 (2021) 1269-1288.
[24] S. Goodarzi, A. Rahi, Optimization of dual dynamic vibration absorber to reduce rotor torsional vibrations, Journal of Vibration and Sound, 13(26) (2025) 3-1.
[25]  J. Taghipour, M. Dardel, M.H. Pashaei, Vibration mitigation of a nonlinear rotor system with linear and nonlinear vibration absorbers, Mechanism and Machine Theory, 128 (2018) 586-615.
[26] Y. Cao, Z. Li, J. Dou, R. Jia, H. Yao, An inerter nonlinear energy sink for torsional vibration suppression of the rotor system, Journal of Sound and Vibration, 537 (2022) 11718.
[27] B. Al-Bedoor, K. Moustafa, K. Al-Hussain, Dual dynamic absorber for the torsional vibrations of synchronous motor-driven compressors, Journal of sound and vibration, 220(4) (1999) 729-748.
[28] J.H. Ginsberg, Advanced engineering dynamics, Cambridge University Press, 1998.
[29] A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008.
[30] A.H. Nayfeh, Perturbation methods in nonlinear dynamics, in:  Lecture Notes in Physics: Nonlinear Dynamics Aspects of Particle Accelerators, Springer, 2007, pp. 238-314.
[31] H. Abundis-Fong, J. Enríquez-Zárate, A. Cabrera-Amado, G. Silva-Navarro, Optimum design of a nonlinear vibration absorber coupled to a resonant oscillator: A case study, Shock and Vibration, 2018(1) (2018) 2107607.
[32] R. Hamming, Numerical methods for scientists and engineers, Courier Corporation, 2012.
[33] R.S. Esfandiari, Numerical methods for engineers and scientists using MATLAB®, Crc Press, 2017.
AUT Journal of Mechanical Engineering
Volume 10, Issue 1
January 2026
Pages 75-88

Files

Share

How to cite

Statistics