Broadband vibration suppression of a nonlinear beam using a fractional-order inerter-assisted tuned mass damper

  • Yogeesh  Nijalingappa orcid

    Department of Mathematics, Government First Grade College, Tumakuru 572102, India; Mathematics & Natural Sciences, Gulf University for Science & Technology, Safat 13060, Kuwait; Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
  • Suleiman Ibrahim  Mohammad orcid

    Department of Mathematics, Government First Grade College, Tumakuru 572102, India; Department of Business Administration, Business School, Al al-Bayt University, Mafraq 25113, Jordan
  • Tarun Madan  Kanade orcid

    Symbiosis Institute of Operations Management, Symbiosis International (Deemed University), Nashik 422008, India
  • Asokan  Vasudevan orcid

    Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
  • P. William orcid

    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, Kelana Jaya 47301, Malaysia
  • Mohammad Faleh  Ahmmad Hunitie orcid

    Department of Public Administration, School of Business, University of Jordan, Amman 11942, Jordan
Article ID: 4497
DOI: https://doi.org/10.59400/sv4497
Keywords: beam vibration, inerter-assisted tuned mass damper, fractional damping, harmonic balance, nonlinear dynamics, passive control, design map

Abstract

This study presents an analytical method for reducing broadband vibration in a simply supported nonlinear beam fitted with an inerter-assisted tuned mass damper. The first bending mode is obtained by Galerkin projection, geometric nonlinearity is represented by a cubic stiffness term, and beam damping is described by a fractional-order derivative. A single-harmonic balance formulation converts the coupled equations into an amplitude-dependent cubic equation that is solved directly over the forcing-frequency range. The absorber is optimized with respect to inertance ratio, tuning ratio, damping ratio, and fractional order. The objective is to minimize the largest beam amplitude between 7 and 14 Hz. For the beam considered, increasing the inertance ratio from 0 to 0.20 raises the peak-response reduction from about 4.5% to about 52%, while the physical absorber mass ratio remains 0.04. The optimal tuning ratio decreases as inertance increases, whereas the required absorber damping generally increases. A ±5% stiffness study shows that the optimized designs remain effective under moderate uncertainty. The results also clarify how fractional damping modifies the balance between effective stiffness and dissipation, enabling the proposed maps to support robust initial absorber selection before detailed high-fidelity validation. The resulting design maps and regression equations provide useful preliminary settings for later finite-element or experimental verification.

Published
2026-07-24
How to Cite
Nijalingappa, Y., Mohammad, S., Kanade, T., Vasudevan, A., P. William, & Ahmmad Hunitie, M. (2026). Broadband vibration suppression of a nonlinear beam using a fractional-order inerter-assisted tuned mass damper. Sound & Vibration, 60(5). https://doi.org/10.59400/sv4497
Issue
Vol. 60 No. 5 (2026): In Progress
Section
Article

Copyright (c) 2026 Yogeesh  Nijalingappa, Suleiman Ibrahim  Mohammad, Tarun Madan  Kanade, Asokan  Vasudevan, P. William, Mohammad Faleh  Ahmmad Hunitie

Creative Commons License

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

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