Interval type-2 fuzzy fractional harmonic-balance optimization of a quasi-zero-stiffness isolator for robust low-frequency vibration suppression

Suleiman Ibrahim Mohammad
Research Fellow, INTI International University, Nilai 71800, Malaysia
Yogeesh Nijalingappa
Research Fellow, INTI International University, Nilai 71800, Malaysia; Mathematics & Natural Sciences, Gulf University for Science & Technology, Safat 13060, Kuwait; Department of Mathematics, Government First Grade College, Tumkur 572102, India
Seif Al Bustanji
Faculty of Technical Education, Al-Ahliyya Amman University, Amman 19328, Jordan; Hourani Center for Applied Scientific Research (HCASR), Al-Ahliyya Amman University, Amman 19328, Jordan
Poornachandran William
School of Computer Science and Technology, Karunya Institute of Technology and Sciences, Coimbatore 641114, India; Centre for Research and Consultancy, UNITAR International University, Petaling Jaya 47301, Malaysia
Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Torki M. Al-Fawwaz
College of Commerce and Business, Lusail University, Lusail P.O. Box 9717, Qatar

Article ID: 4679

Keywords: quasi-zero stiffness; fractional calculus; interval type-2 fuzzy set; harmonic balance; robust optimization; nonlinear vibration isolation; epistemic uncertainty

Abstract

Quasi-zero-stiffness (QZS) isolators possess a combination of high load capacity and low dynamic stiffness; however, their characteristics are sensitive to geometric nonlinearity, frequency-dependent dissipation, excitation amplitude and epistemic uncertainty. In this study, a new design scheme is proposed to produce the constant geometric restoring force of a three-spring QZS isolator subject to base excitation. Caputo fractional damping + exact first-harmonic stiffness (in terms of complete elliptic integrals) + multi-harmonic alternating frequency–time harmonic balance (to check the harmonic content and residual error). Interval type-2 fuzzy numbers account for uncertainty in the following quantities: geometric ratio, residual tangent stiffness, fractional damping intensity (or order), and base-motion amplitude. Differential evolution of upper-tail resonance risk and lower-tail isolation losses. A limiting-case validation against a literature benchmark verifies that the fractional-order models recover the classic viscously damped three-spring QZS equations for the case of approaching finite response amplitude and unity fractional order. For the 50 kg realization, the optimized design has a geometric ratio of 1.1824, residual stiffness of 0.02110, damping ratio of 0.02581 and fractional order of 0.9063. Its 95th-percentile peak transmissibility is 3.358 across 120 outer-footprint scenarios, which is 28.9% below the optimized viscous-limit QZS reference. Adverse-tail isolation onset is 23.3% earlier than deterministic fractional tuning completion, and adverse-tail mean attenuation improvements are as high as 1.08 dB. The five-harmonic verification ensures that the ratio of the third harmonic stays below 0.31% in all ranges mentioned in operating range.

Published

2026-09-01

How to Cite

Mohammad, S. I., Nijalingappa, Y., Bustanji, S. A., William, P., Vasudevan, A., & Al-Fawwaz, T. M. (2026). Interval type-2 fuzzy fractional harmonic-balance optimization of a quasi-zero-stiffness isolator for robust low-frequency vibration suppression. Sound & Vibration, 60(6). https://doi.org/10.59400/sv4679

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Vol. 60 No. 6 (2026): In Progress

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Article

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

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Interval type-2 fuzzy fractional harmonic-balance optimization of a quasi-zero-stiffness isolator for robust low-frequency vibration suppression

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