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<p>This work analyses the out-of-plane free vibration behaviour of Power-law Functionally Graded Material (PFGM) plates using the Dynamic Stiffness Method (DSM). The material properties of the PFGM vary continuously along the thickness direction, following a power-law distribution in terms of the volume fractions of the constituent materials. Hamilton’s principle is employed to derive the governing partial differential equations of motion, based on Classical Plate Theory (CPT). Unlike conventional CPT applications, the present formulation considers the physical neutral surface instead of the plate’s geometric mid-surface for improved accuracy in material gradation. The dynamic stiffness matrix for the PFGM plate is constructed using this formulation, and the well-known Wittrick–Williams (W–W) algorithm is utilized to solve the resulting transcendental eigenvalue problem and extract the natural frequencies. The DSM predictions show excellent consistency, with deviations typically within 1–2% when validated against reliable benchmark data. However, it is observed that certain published results exhibit noticeable discrepancies and appear to lack the desired level of accuracy. Furthermore, a parametric study is conducted to investigate the influence of various parameters–such as aspect ratio, volume fraction index, and boundary conditions–on the natural frequencies of the PFGM plates. The high accuracy of the proposed method suggests that it can serve as a benchmark solution for future studies on PFGM plates.</p>

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Free vibration analysis of functionally graded plates with variable boundary conditions considering physical neutral surface

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Manish Chauhan,
  • Vinayak Ranjan,
  • Baij Nath Singh,
  • R N Hota

摘要

This work analyses the out-of-plane free vibration behaviour of Power-law Functionally Graded Material (PFGM) plates using the Dynamic Stiffness Method (DSM). The material properties of the PFGM vary continuously along the thickness direction, following a power-law distribution in terms of the volume fractions of the constituent materials. Hamilton’s principle is employed to derive the governing partial differential equations of motion, based on Classical Plate Theory (CPT). Unlike conventional CPT applications, the present formulation considers the physical neutral surface instead of the plate’s geometric mid-surface for improved accuracy in material gradation. The dynamic stiffness matrix for the PFGM plate is constructed using this formulation, and the well-known Wittrick–Williams (W–W) algorithm is utilized to solve the resulting transcendental eigenvalue problem and extract the natural frequencies. The DSM predictions show excellent consistency, with deviations typically within 1–2% when validated against reliable benchmark data. However, it is observed that certain published results exhibit noticeable discrepancies and appear to lack the desired level of accuracy. Furthermore, a parametric study is conducted to investigate the influence of various parameters–such as aspect ratio, volume fraction index, and boundary conditions–on the natural frequencies of the PFGM plates. The high accuracy of the proposed method suggests that it can serve as a benchmark solution for future studies on PFGM plates.