Representation-Theoretic Symmetry Reduction and Fuzzy-Grey Optimization of Modular Vibration Systems

Year : 2026 | Volume : 02 | Issue : 01 | Page : 22 30
    By

    Tejas Bhushan N.B.,

  • Markala Karthik,

  • Mohammed Almakki,

  • Mohammed El Khider,

  1. Research Student, Department of Chemistry, Regional Institute of Education (NCERT), Karnataka, India
  2. Assistant Professor, Department of Electrical and Electronics Engineering, SR University, Telangana, India
  3. Assistant Professor, School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai, United Arab Emirates
  4. Assistant Professor, Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai, United Arab Emirates

Abstract

This paper presents a representation-theoretic framework for symmetry-aware vibration control in modular structural systems. Exploiting cyclic symmetry, the mass, damping, and stiffness operators are block-diagonalised into irreducible representations, reducing the full structural dynamics to a collection of lower-dimensional modal subsystems. This decomposition provides both computational efficiency and a rigorous mathematical description of symmetry-preserving dynamic behaviour. To account for imperfections arising in practical implementations, near-symmetry defects in stiffness and damping are quantified using projector-based measures defined on the corresponding invariant subspaces. An uncertainty band is introduced to model manufacturing tolerances, parameter variability, and control-induced perturbations, enabling the analysis of structural performance under bounded uncertainty. The resulting formulation captures deviations from ideal symmetry while retaining the underlying algebraic structure of the system. A multi-criteria optimisation framework is then developed to balance vibration attenuation, control effort, and symmetry preservation. These competing objectives are integrated through a fuzzy-grey relational model, producing a mathematically explicit objective function suitable for robust design and parameter tuning. The optimisation process identifies solutions that simultaneously enhance damping performance and limit symmetry degradation in the presence of uncertainty. A numerical study involving a six-module cyclic ring structure illustrates the effectiveness of the proposed approach. Results show that both symmetry-reduced retuning and the fuzzy-grey optimal design significantly improve vibration suppression compared with the baseline configuration. Moreover, the fuzzy-grey optimum achieves additional reductions in symmetry defect while maintaining favourable control characteristics. The proposed framework contributes an ETSY-aligned methodology in which symmetry, uncertainty quantification, and optimisation are unified through algebraic operators, representation theory, and high-density mathematical formulations, providing a systematic foundation for the design of robust modular structural systems.

Keywords: Symmetry reduction, cyclic representation, vibration control, fuzzy-grey optimisation, modular structures, uncertainty bands

[This article belongs to Emerging Trends in Symmetry ]

How to cite this article:
Tejas Bhushan N.B., Markala Karthik, Mohammed Almakki, Mohammed El Khider. Representation-Theoretic Symmetry Reduction and Fuzzy-Grey Optimization of Modular Vibration Systems. Emerging Trends in Symmetry. 2026; 02(01):22-30.
How to cite this URL:
Tejas Bhushan N.B., Markala Karthik, Mohammed Almakki, Mohammed El Khider. Representation-Theoretic Symmetry Reduction and Fuzzy-Grey Optimization of Modular Vibration Systems. Emerging Trends in Symmetry. 2026; 02(01):22-30. Available from: https://journals.stmjournals.com/etsy/article=2026/view=247482


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Regular Issue Subscription Review Article
Volume 02
Issue 01
Received 14/03/2026
Accepted 22/04/2026
Published 30/04/2026
Publication Time 47 Days
1

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