Possibility-based transfer-matrix optimization of a graded double-cavity micro-perforated partition with fuzzy parameters for broadband sound transmission loss

Yogeesh Nijalingappa
Department of Mathematics, Government First Grade College, Tumakuru 572102, India; Research Fellow, INTI International University, Nilai 71800, Malaysia
Naeema Darwish Khamis Al Maashari
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Chethana N. S.
Department of Mathematics, Central University of Karnataka, Kalaburagi 585367, India
Wenya Wu
Faculty of Business and Communications, Xingtai Vocational College of Applied Technology, Xingtai 054000, China
Sulieman Ibrahim Mohammad
Research Fellow, INTI International University, Nilai 71800, Malaysia; Department of Business Administration, Business School, Al al-Bayt University, Mafraq 25113, Jordan
Mohammad Faleh Ahmmad Hunitie
Department of Public Administration, School of Business, University of Jordan, Amman 11942, Jordan

Article ID: 4292

Keywords: fuzzy mathematics, micro-perforated panel, possibility theory, graded cavity, transfer matrix, sound transmission loss, robust acoustic design

Abstract

This study proposes a possibility-based transfer-matrix optimization and assessment framework for fuzzy geometric parameters in a graded double-cavity micro-perforated partition. The system consists of a front limp panel, a first air cavity, a micro-perforated panel, a second air cavity, and a back limp panel. The two cavities are graded over three equal parallel strips, so the local depths of the two cavities differ from strip to strip. Fuzzy numbers model each uncertain design quantity as a triangular fuzzy number and propagate through alpha-cuts. The acoustic model consists of explicit transfer matrices, an area-averaged transmission coefficient, and normal-incidence sound transmission loss. The specific novelty is the direct use of exact alpha-cut corner propagation inside the graded strip-wise transfer-matrix objective, where guaranteed band-average sound transmission loss, guaranteed low-band minimum, and fuzzy width are evaluated together rather than only after a deterministic design is selected. A fuzzy width penalty and guaranteed band-average transmission loss with guaranteed low-band minimum transmission loss are included in the objective function. This is analyzed with a detailed numerical study from 250 Hz to 2,000 Hz. The selected graded design realizes a guaranteed average sound transmission loss of 78.085 dB and a guaranteed low-band minimum of 41.323 dB, while the central design gives 81.425 dB and 43.406 dB, respectively. Compared with a uniform-cavity reference evaluated under the same fuzzy setting, the graded design improves the guaranteed low-band average and minimum while maintaining a comparable uncertainty width. This study focuses on mathematical formulation, tabulated numerical output, and an accessible interpretation of design rather than a long theoretical discussion.

Published

2026-07-21

How to Cite

Nijalingappa, Y., Khamis Al Maashari, N. D., Vasudevan, A., N. S., C., Wu , W., Ibrahim Mohammad, S., & Ahmmad Hunitie, M. F. (2026). Possibility-based transfer-matrix optimization of a graded double-cavity micro-perforated partition with fuzzy parameters for broadband sound transmission loss. Sound & Vibration, 60(4). https://doi.org/10.59400/sv4292

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Vol. 60 No. 4 (2026)

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Article

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

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