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<p>This paper presents a geometry constrained optimization framework for the design of dual beam-based Tuned Mass Dampers (TMDs) to mitigate coupled bending–torsion vibrations in cantilever plates. Unlike conventional tuning methods that optimize stiffness as an independent variable, this study derives each absorber’s stiffness from Euler–Bernoulli beam theory and includes its self-mass through a first-mode modal mass correction, explicitly enforcing manufacturing constraints related to slenderness ratio and static tip deflection. A reduced order four-degree-of-freedom (4-DOF) model is employed to represent the coupled dynamics of the host structure and the absorbers. The model parameters are obtained from analytical plate theory and validated against a finite element model in ANSYS with frequency errors below 0.2%. A six-mode truncation study confirms that two modes are sufficient within the target frequency band. A multiobjective genetic algorithm is used to comparatively evaluate three design strategies: classical frequency matching, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {H}_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> peak minimization, and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {H}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> RMS minimization, ensuring a fair and consistent comparison. A normalized Pareto selection criterion is introduced to prevent bias toward the higher-amplitude bending mode, and a sensitivity analysis with multiple independent genetic algorithm runs is conducted to ensure statistical reliability of the results. The simulation results demonstrate the importance of geometric feasibility in practical TMD optimization and show how the three tuning strategies differ under impulse, harmonic, and broadband excitation for lightweight plate-like structures.</p>

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Multiobjective optimal design of beam-based tuned mass dampers for coupled plate vibrations

  • 期刊论文

  • 发表日期：

    2026年8月2日

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  • Erdi Gulbahce

摘要

This paper presents a geometry constrained optimization framework for the design of dual beam-based Tuned Mass Dampers (TMDs) to mitigate coupled bending–torsion vibrations in cantilever plates. Unlike conventional tuning methods that optimize stiffness as an independent variable, this study derives each absorber’s stiffness from Euler–Bernoulli beam theory and includes its self-mass through a first-mode modal mass correction, explicitly enforcing manufacturing constraints related to slenderness ratio and static tip deflection. A reduced order four-degree-of-freedom (4-DOF) model is employed to represent the coupled dynamics of the host structure and the absorbers. The model parameters are obtained from analytical plate theory and validated against a finite element model in ANSYS with frequency errors below 0.2%. A six-mode truncation study confirms that two modes are sufficient within the target frequency band. A multiobjective genetic algorithm is used to comparatively evaluate three design strategies: classical frequency matching, \(\mathcal {H}_{\infty }\) H ∞ peak minimization, and \(\mathcal {H}_{2}\) H 2 RMS minimization, ensuring a fair and consistent comparison. A normalized Pareto selection criterion is introduced to prevent bias toward the higher-amplitude bending mode, and a sensitivity analysis with multiple independent genetic algorithm runs is conducted to ensure statistical reliability of the results. The simulation results demonstrate the importance of geometric feasibility in practical TMD optimization and show how the three tuning strategies differ under impulse, harmonic, and broadband excitation for lightweight plate-like structures.