Alpha-cut robust design of a fractional-order fuzzy tuned mass damper for targeted-band vibration suppression in rotating machinery

Yogeesh Nijalingappa
Department of Mathematics, Government First Grade College, Tumkur 572102, India; Mathematics and Natural Sciences, Gulf University for Science and Technology, Safat 13060, Kuwait; Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Tahir Muhammad Ali
Department of Computer Science, Gulf University for Sciences and Technology, Safat 13060, Kuwai
Rajashree Jain
Symbiosis Institute of Computer Studies and Research, Symbiosis International (Deemed University), Pune 411016, India
P. William
School of Computer Science and Technology, Karunya Institute of Technology and Sciences (Deemed University), Coimbatore 641114, India; Centre for Research and Consultancy, UNITAR International University, Petaling Jaya 47301, Malaysia

Article ID: 4626

Keywords: fractional damping; alpha-cut; robust tuned mass damper; interval response; rotating machinery

Abstract

This study presents a targeted-band design method for suppressing flexible-rotor vibration using a fractional-order fuzzy tuned mass damper. A force-excited rotor-support mode represents the host machine, while the absorber branch comprises a spring and fractional dashpot. The absorber parameters are selected to minimize the primary displacement peak while remaining robust to bounded uncertainty in mass ratio, tuning ratio, damping index, fractional order, support stiffness, and force level. Triangular fuzzy numbers are propagated through alpha-cut intervals, and the resulting frequency-response envelopes are optimized by a weighted objective that penalizes high peaks and wide uncertainty spreads. Closed-form frequency-response relations evaluated directly at interval corners keep the procedure transparent and reproducible. For a rotor-support oscillator with natural frequency 9.762 Hz, primary mass 42 kg, primary stiffness 158,000 N/m, force amplitude 58 N, and mass ratio μ = 0.05, the optimized design yields a central peak displacement of 1.929 mm and an alpha-zero upper peak of 3.154 mm, compared with 10.197 mm for the uncontrolled system and 2.028 mm for the deterministic Den Hartog reference. Evaluation at μ = 0.03, 0.05, and 0.07 shows consistent peak reduction and useful trends for initial parameter tuning. The method therefore provides bounded vibration envelopes, tuning guidance, stroke estimates, and sensitivity rankings for uncertain rotating-machine data within the specified target band.

Published

2026-08-16

How to Cite

Nijalingappa, Y., Vasudevan, A., Muhammad Ali, T., Jain, R., & William, P. (2026). Alpha-cut robust design of a fractional-order fuzzy tuned mass damper for targeted-band vibration suppression in rotating machinery. Sound & Vibration, 60(5). https://doi.org/10.59400/sv4626

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Vol. 60 No. 5 (2026): In Progress

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Zadeh LA. Fuzzy Sets. Information and Control. 1965; 8(3): 338–353. doi: 10.1016/S0019-9958(65)90241-X

[2]Zadeh LA. Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems. 1978; 1(1): 3–28. doi: 10.1016/0165-0114(78)90029-5

[3]Dubois D, Prade H. Operations on Fuzzy Numbers. International Journal of Systems Science. 1978; 9(6): 613–626. doi: 10.1080/00207727808941724

[4]Hanss M. The Transformation Method for the Simulation and Analysis of Systems with Uncertain Parameters. Fuzzy Sets and Systems. 2002; 130(3): 277–289. doi: 10.1016/S0165-0114(02)00045-3

[5]Hanss M. The Extended Transformation Method for the Simulation and Analysis of Fuzzy-Parameterized Models. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 2003; 11(6): 711–727. doi: 10.1142/S0218488503002491

[6]Moens D, Vandepitte D. A Fuzzy Finite Element Method for Frequency Response Function Analysis of Uncertain Structures. AIAA Journal. 2002; 40(1): 126–136. doi: 10.2514/2.1621

[7]Giannini O, Hanss M. The Component Mode Transformation Method: A Fast Implementation of Fuzzy Arithmetic for Uncertainty Management in Structural Dynamics. Journal of Sound and Vibration. 2008; 311(3–5): 1340–1357. doi: 10.1016/j.jsv.2007.10.029

[8]Adhikari S, Chowdhury R, Friswell MI. High Dimensional Model Representation Method for Fuzzy Structural Dynamics. Journal of Sound and Vibration. 2011; 330(7): 1516–1529. doi: 10.1016/j.jsv.2010.10.010

[9]Balu AS, Rao BN. Efficient Explicit Formulation for Practical Fuzzy Structural Analysis. Sadhana. 2011; 36: 463–488. doi: 10.1007/s12046-011-0035-3

[10]Balu AS, Rao BN. High Dimensional Model Representation Based Formulations for Fuzzy Finite Element Analysis of Structures. Finite Elements in Analysis and Design. 2012; 50: 217–230. doi: 10.1016/j.finel.2011.09.012

[11]Xu M, Wang X, Qiu Z. A Dual-Layer Dimension-Wise Fuzzy Finite Element Method for Structural Analysis with Epistemic Uncertainties. Fuzzy Sets and Systems. 2019; 367: 68–81. doi: 10.1016/j.fss.2018.08.010

[12]Patle BK, Hirwani CK, Singh RP, et al. Eigenfrequency and Deflection Analysis of Layered Structure Using Uncertain Elastic Properties: A Fuzzy Finite Element Approach. International Journal of Approximate Reasoning. 2018; 98: 163–176. doi: 10.1016/j.ijar.2018.04.013

[13]Silva ADG, Cavalini AA, Steffen V. Fuzzy Robust Design of Dynamic Vibration Absorbers. Shock and Vibration. 2016; 2016: 2081518. doi: 10.1155/2016/2081518

[14]Smith MC. Synthesis of Mechanical Networks: The Inerter. IEEE Transactions on Automatic Control. 2002; 47(10): 1648–1662. doi: 10.1109/TAC.2002.803532

[15]Smith MC, Wang FC. Performance Benefits in Passive Vehicle Suspensions Employing Inerters. Vehicle System Dynamics. 2004; 42: 235–257. doi: 10.1080/00423110412331289871

[16]Chen MZQ, Papageorgiou C, Scheibe F, et al. The Missing Mechanical Circuit Element. IEEE Circuits and Systems Magazine. 2009; 9(1): 10–26. doi: 10.1109/MCAS.2008.931738

[17]Hu Y, Chen MZQ, Shu Z. Passive Vehicle Suspensions Employing Inerters with Multiple Performance Requirements. Journal of Sound and Vibration. 2014; 333(8): 2212–2225. doi: 10.1016/j.jsv.2013.12.016

[18]Shen Y, Chen L, Yang X, et al. Improved Design of Dynamic Vibration Absorber by Using the Inerter and Its Application in Vehicle Suspension. Journal of Sound and Vibration. 2016; 361: 148–158. doi: 10.1016/j.jsv.2015.06.045

[19]Ma R, Bi K, Hao H. Inerter-Based Structural Vibration Control: A State-of-the-Art Review. Engineering Structures. 2021; 243: 112655. doi: 10.1016/j.engstruct.2021.112655

[20]Liu C, Chen L, Lee HP, et al. A Review of the Inerter and Inerter-Based Vibration Isolation: Theory, Devices, and Applications. Journal of the Franklin Institute. 2022; 359(14): 7677–7707. doi: 10.1016/j.jfranklin.2022.07.030

[21]Bagley RL, Torvik PJ. Fractional Calculus: A Different Approach to the Analysis of Viscoelastically Damped Structures. AIAA Journal. 1983; 21(5): 741–748. doi: 10.2514/3.8142

[22]Rüdinger F. Tuned Mass Damper with Nonlinear Viscous Damping. Journal of Sound and Vibration. 2007; 300(3–5): 932–948. doi: 10.1016/j.jsv.2006.09.009

[23]Muresan CI, Folea S, Birs IR, et al. A Novel Fractional-Order Model and Controller for Vibration Suppression in a Flexible Smart Beam. Nonlinear Dynamics. 2018; 93(2): 525–541. doi: 10.1007/s11071-018-4207-0

[24]Xu J, Chen Y, Tai Y, et al. Vibration Analysis of Complex Fractional Viscoelastic Beam Structures by the Wave Method. International Journal of Mechanical Sciences. 2020; 167: 105204. doi: 10.1016/j.ijmecsci.2019.105204

[25]Sun X, Zhu A, Yin Z, et al. Hermite Finite Element Method for a Time-Fractional Order Damping Beam Vibration Problem. Fractal and Fractional. 2023; 7(10): 739. doi: 10.3390/fractalfract7100739

[26]Guo R, Meng N, Wang J, et al. Response Analysis and Vibration Suppression of Fractional Viscoelastic Shape Memory Alloy Spring Oscillator under Harmonic Excitation. Axioms. 2024; 13(11): 803. doi: 10.3390/axioms13110803

[27]Das A, Banerjee A, Sahoo DR, et al. Inerter-based tuned mass dampers for response control of multi-degree-of-freedom structures subjected to wind and earthquake excitations. Structure and Infrastructure Engineering. 2026; 22(4): 624–637. doi: 10.1080/15732479.2024.2345280

[28]Peng Y, Sun P. Reliability-Based Design Optimization of Tuned Mass-Damper-Inerter for Mitigating Structural Vibration. Journal of Sound and Vibration. 2024; 572: 118166. doi: 10.1016/j.jsv.2023.118166

[29]Nesić N, Karličić D, Cajić M, et al. Vibration Suppression of a Platform by a Fractional Type Electromagnetic Damper and Inerter-Based Nonlinear Energy Sink. Applied Mathematical Modelling. 2025; 137: 115651. doi: 10.1016/j.apm.2024.115651

[30]Sofi A, Muscolino G, Di Paola M. Reliability Analysis of Structures Controlled by External Fractional Viscoelastic Dampers with Interval Parameters. Acta Mechanica Sinica. 2023; 39: 722486. doi: 10.1007/s10409-023-22486-x

[31]Yang F, Sedaghati R, Esmailzadeh E. Vibration Suppression of Structures Using Tuned Mass Damper Technology: A State-of-the-Art Review. Journal of Vibration and Control. 2022; 28(7–8): 812–836. doi: 10.1177/1077546320984305

[32]Aydın Y, Bekdaş G, Nigdeli SM, et al. Adaptive Harmony Search-Based Optimization of Tuned Mass Damper Inerters under Near-Fault Earthquake Records. GeoHazards. 2025; 6(3): 56. doi: 10.3390/geohazards6030056

[33]Sun P, Peng Y. Reliability-Informed Design Table for Optimizing Tuned Mass-Damper-Inerter Systems to Improve Structural Seismic Performance. Probabilistic Engineering Mechanics. 2025; 80: 103769. doi: 10.1016/j.probengmech.2025.103769

[34]Cai J, Gao Q, Liu Y, et al. Control Design, Analysis, and Optimization of Fractional-Order Delayed Resonator for Complete Vibration Absorption. Journal of Sound and Vibration. 2024; 571: 118083. doi: 10.1016/j.jsv.2023.118083

[35]Jafarzadeh O, Sabetahd R, Ghasemi SAM, et al. Design of a Novel Intelligent Adaptive Fractional-Order Proportional-Integral-Derivative Controller for Mitigation of Seismic Vibrations of a Building Equipped with an Active Tuned Mass Damper. Smart Materials and Structures. 2024; 33(9): 095020. doi: 10.1088/1361-665X/ad67bc

[36]Ouzizi A, Belkourchia Y, Abdoun F, et al. Vibration Suppression of Periodically Loaded Beams Using Optimized Fractional Dynamic Vibration Absorbers. Journal of Vibration and Control. 2025. doi: 10.1177/10775463251364512

[37]Li J, Sun Y, Liu X, et al. Tuning Mechanism and Parameter Optimization of a Dynamic Vibration Absorber with Inerter and Negative Stiffness Under Delayed FOPID. Mathematics. 2025; 13(13): 2124. doi: 10.3390/math13132124

[38]Den Hartog JP. The Amplitudes of Non-Harmonic Vibrations. Journal of the Franklin Institute. 1933; 216(4): 459–473. doi: 10.1016/S0016-0032(33)90915-1

[39]Aydın Y, Bekdaş G, Nigdeli SM, et al. Parameter Optimization of Tuned Mass Damper Inerter via Adaptive Harmony Search. Computer Modeling in Engineering & Sciences. 2024; 141(3): 2471–2499. doi: 10.32604/cmes.2024.056693

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Alpha-cut robust design of a fractional-order fuzzy tuned mass damper for targeted-band vibration suppression in rotating machinery

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