Nonsmooth Chebyshev H-infinity optimization of sparse inerter-dashpot absorber networks for broadband plate vibration suppression

Yogeesh Nijalingappa
Department of Mathematics & Natural Sciences, Gulf University for Science & Technology, Safat 13060, Kuwait; Department of Mathematics, Government First Grade College, Tumkur 572102, India; Research Fellow, INTI International University, Nilai 71800, Malaysia
Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Rashed Abu Hammour
Faculty of Technical Education, Hourani Center for Applied Scientific Research (HCASR), Al-Ahliyya Amman University, Amman 19111, Jordan
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
Tejas Bhushan N. B
Department of Chemistry, Regional Institute of Education (NCERT), Mysuru 570006, India
Suleiman Ibrahim Mohammad
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: 4755

Keywords: mathematical optimization; Chebyshev minimax design; H-infinity vibration control; inerter-dashpot absorber; plate mobility; nonsmooth optimization; passive vibration attenuation

Abstract

This paper develops a mathematical optimization framework for broadband vibration attenuation of a simply supported thin plate using a sparse network of passive inerter-dashpot dynamic absorbers. The four attachment locations are fixed a priori away from nodal lines of the retained low-order modes; the optimizer allocates a total absorber mass limited to 4.2% of the plate mass and constrains tuning frequency to 75–580 Hz, damping ratio to 0.035–0.290, and inertance ratio to 0.05–4.50 over the selected 45–650 Hz numerical band. A modal Kirchhoff–Love model is condensed with frequency-dependent absorber impedances, and a nonsmooth Chebyshev H-infinity epigraph objective is treated by log-sum-exp smoothing, differential-evolution exploration, and projected local polishing. For the ten-mode benchmark, the robust design reduces nominal peak mobility from 91.889 dB to 85.096 dB: its 6.793 dB reduction exceeds modal tuning by 0.468 dB and the uniform-inerter layout by 1.604 dB. Across fifty material-and-damping perturbation scenarios, its 95th-percentile peak is 1.757 dB below modal tuning, indicating a practically relevant upper-tail benefit, although experimental validation remains necessary. Because the tenth retained plate mode is 385.356 Hz, results above that frequency are reported as exploratory pending a 15–20-mode convergence study.

Published

2026-09-04

How to Cite

Nijalingappa, Y., Vasudevan, A., Hammour, R. A., William, P., N. B, T. B., Mohammad, S. I., & Al-Fawwaz, T. M. (2026). Nonsmooth Chebyshev H-infinity optimization of sparse inerter-dashpot absorber networks for broadband plate vibration suppression. Sound & Vibration, 60(6). https://doi.org/10.59400/sv4755

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

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

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Nonsmooth Chebyshev H-infinity optimization of sparse inerter-dashpot absorber networks for broadband plate vibration suppression

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