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<p>Spectral data with partial information is incorporated in this study to develop a systematic approach for refining symmetric structured finite element models, where certain eigenvalues and specific entries of the corresponding eigenvectors are prescribed. The approach ensures the preservation of the symmetric structural integrity of the system, avoids spillover effects, and minimizes perturbations to the mass and stiffness matrices. Inspired by recent advancements in the updating of the symmetric finite element models, we establish necessary and sufficient conditions for the existence of solutions and characterize all possible solutions. The problem is then formulated as a constrained optimization, seeking minimal perturbations to the system matrices that enforces the prescribed spectral properties while maintaining no spillover. Numerical examples are presented to demonstrate the effectiveness of the method, with comparisons that highlight its robustness and advantages in dynamic system analysis.</p>

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An optimization framework for spillover-free updating of symmetric finite element models with incomplete spectral data

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • H. Lalhriatpuia,
  • Tanay Saha

摘要

Spectral data with partial information is incorporated in this study to develop a systematic approach for refining symmetric structured finite element models, where certain eigenvalues and specific entries of the corresponding eigenvectors are prescribed. The approach ensures the preservation of the symmetric structural integrity of the system, avoids spillover effects, and minimizes perturbations to the mass and stiffness matrices. Inspired by recent advancements in the updating of the symmetric finite element models, we establish necessary and sufficient conditions for the existence of solutions and characterize all possible solutions. The problem is then formulated as a constrained optimization, seeking minimal perturbations to the system matrices that enforces the prescribed spectral properties while maintaining no spillover. Numerical examples are presented to demonstrate the effectiveness of the method, with comparisons that highlight its robustness and advantages in dynamic system analysis.