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Background <p>Traditional displacement-based models often struggle to accurately capture the complex behavior of laminated composite plates. Specifically, there is a persistent need for higher-order kinematic models that can account for the parabolic distribution of transverse shear stresses across a plate's thickness without relying on empirical adjustments.</p> Purpose <p>The primary objective of this study is to conduct a free vibration analysis of laminated composite plates using a refined hyperbolic shear deformation theory. This theory is specifically designed to satisfy zero shear stress conditions at the top and bottom surfaces of the plate, thereby eliminating the need for empirical shear correction factors. Additionally, by optimizing the kinematic model, the theory reduces the number of independent unknowns, which significantly enhances computational efficiency while maintaining high levels of accuracy for structural analysis.</p> Methods <p>To define the plate's dynamics, the researchers utilized a rigorous mathematical approach centered on variational mechanics, where the governing equations of motion were derived by considering variations in kinetic energy, strain potential energy, and the work done by non-conservative forces. The study specifically focuses on simply supported, rectangular, cross-ply laminated plates, applying a refined hyperbolic kinematics model to ensure accurate stress distribution modeling throughout the plate’s thickness. This sophisticated shear deformation model allows for a more precise representation of structural behavior without the limitations of simpler, traditional theories.</p> Conclusions <p>The study validated the proposed theory through extensive numerical benchmarks against established literature, demonstrating that the refined hyperbolic model achieves a high degree of numerical accuracy in predicting natural frequencies. The results indicate that the theory performs reliably across various aspect ratios, proving to be a precise and computationally efficient framework for the design and study of advanced composite structures.</p>

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Vibration Analysisofcross-Ply Laminatedcomposite Plates Using Refined Theory with Dual Variables

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Lairedj Abdelaziz,
  • Rami K. Suleiman,
  • Mohammed Hadj Meliani

摘要

Background

Traditional displacement-based models often struggle to accurately capture the complex behavior of laminated composite plates. Specifically, there is a persistent need for higher-order kinematic models that can account for the parabolic distribution of transverse shear stresses across a plate's thickness without relying on empirical adjustments.

Purpose

The primary objective of this study is to conduct a free vibration analysis of laminated composite plates using a refined hyperbolic shear deformation theory. This theory is specifically designed to satisfy zero shear stress conditions at the top and bottom surfaces of the plate, thereby eliminating the need for empirical shear correction factors. Additionally, by optimizing the kinematic model, the theory reduces the number of independent unknowns, which significantly enhances computational efficiency while maintaining high levels of accuracy for structural analysis.

Methods

To define the plate's dynamics, the researchers utilized a rigorous mathematical approach centered on variational mechanics, where the governing equations of motion were derived by considering variations in kinetic energy, strain potential energy, and the work done by non-conservative forces. The study specifically focuses on simply supported, rectangular, cross-ply laminated plates, applying a refined hyperbolic kinematics model to ensure accurate stress distribution modeling throughout the plate’s thickness. This sophisticated shear deformation model allows for a more precise representation of structural behavior without the limitations of simpler, traditional theories.

Conclusions

The study validated the proposed theory through extensive numerical benchmarks against established literature, demonstrating that the refined hyperbolic model achieves a high degree of numerical accuracy in predicting natural frequencies. The results indicate that the theory performs reliably across various aspect ratios, proving to be a precise and computationally efficient framework for the design and study of advanced composite structures.