Grouped inerter-resonator arrays for broadband reduction of plate mobility and radiated sound power using modal receptance synthesis

  • Yogeesh Nijalingappa orcid

    Department of Mathematics, Government First Grade College, Tumkur 572102, India; Research Fellow, INTI International University, Nilai 71800, Malaysia
  • Asokan Vasudevan orcid

    Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
  • Mustafa Abdullah

    Hourani Center for Applied Scientific Research, Faculty of Engineering, Al-Ahliyya Amman University, Amman 19111, Jordan
  • Shankaralingappa Bheemasandra Marulappa orcid

    Department of Mathematics, Government First Grade College for Women, Hassan 573201, India
  • Suleiman Ibrahim Mohammad orcid

    Research Fellow, INTI International University, Nilai 71800, Malaysia
  • Ashalatha Kodihalli Siddagangaiah orcid

    Department of Mathematics, Vedavathi Government First Grade College, Hiriyur 577598, India
Article ID: 4199
DOI: https://doi.org/10.59400/sv4199
Keywords: vibration control; inerter-resonator array; plate vibration; metamaterial plate; modal receptance; dynamic stiffness; radiated sound power

Abstract

A plate-type vibroacoustic treatment is developed in which a simply supported Kirchhoff plate is coupled to a grouped array of parallel spring-damper-mass-inerter attachments. The emphasis is intentionally computational. The plate equation is reduced to a modal receptance form using 36 orthogonal sine modes, and the local attachments are eliminated analytically so that each attachment contributes a rank-one dynamic stiffness term. The resulting frequency-domain matrix remains explicit and can therefore be evaluated over large parameter grids without rederiving the governing equations. For the present plate, the bending rigidity is , the areal density is , the planform area is , and the total plate mass is . The sixteen attachments are arranged on a  grid and grouped columnwise at target frequencies, which are  Hz. With the reference internal mass , inertance ratio , tuning scale 0.9, spread coefficient 0.18, and damping ratio , the grouped inerter-resonator array yields average reductions of  dB in point mobility and  dB in both mean-square velocity and radiated sound-power proxy over 80–600 Hz. The spring-mass reference under identical internal mass produces corresponding lower averages of  and  dB. As per this study, the peak-by-peak reductions exceed 20 dB at several dominant modal peaks, while tuning scatter of 5% root-mean-square leaves the average velocity reduction essentially unchanged.

Published
2026-06-09
How to Cite
Nijalingappa, Y., Vasudevan, A., Abdullah, M., Bheemasandra Marulappa, S., Ibrahim Mohammad, S., & Kodihalli Siddagangaiah, A. (2026). Grouped inerter-resonator arrays for broadband reduction of plate mobility and radiated sound power using modal receptance synthesis. Sound & Vibration, 60(3). https://doi.org/10.59400/sv4199
Issue
Vol. 60 No. 3 (2026): In Progress
Section
Article

Copyright (c) 2026 Yogeesh Nijalingappa, Mustafa Abdullah, Asokan Vasudevan, Shankaralingappa Bheemasandra Marulappa, Suleiman Ibrahim Mohammad, Ashalatha Kodihalli Siddagangaiah

Creative Commons License

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

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