Numerical Modeling for the Vibration Characteristics of Multistrata Composite Annular Disks of Spatially Uniform and Nonuniform Thickness Using Refined Higher-Order Shear Deformation Theory

Saira Javed and Asma Khalid

Journal of Mathematics, 2026, vol. 2026, 1-22

Abstract: This study introduces a novel numerical modeling of multistrata composite annular disks of spatially uniform and nonuniform thickness based on refined higher-order shear deformation theory (HSDT), extending beyond conventional single-layer and functionally graded models. The proposed approach uniquely combines layer-wise material discontinuity with thickness variation using an efficient spline-based semianalytical method. The formulation accounts for transverse shear deformation effects without the need for shear correction factors, providing improved accuracy for moderately thick plates. The governing equations of motion are derived using Hamilton’s principle, incorporating the effects of thickness variation, boundary conditions, and material gradation. The thickness of the plate is considered to vary linearly, exponentially, and sinusoidally along the radial direction, allowing the model to capture realistic geometric configurations. The displacement field includes higher-order terms through the thickness, ensuring continuity of transverse stresses at the plate surfaces. The resulting coupled differential equations are solved using a spline numerical technique. The accuracy of the present formulation is validated through already existing results. Parametric studies are performed to examine the influence of geometric ratios, boundary conditions, material properties, and thickness variation on the natural frequencies of the annular disks. The results reveal that variable thickness and shear deformation effects significantly influence the dynamic response, particularly for thick configurations. Results conclude that the effect of the radii ratio β on the angular frequency clearly demonstrates that variable thickness significantly improves angular frequency, especially for thin annular disks β ⟶ 1. Fiber direction and bending stiffness dominate modal stiffness λ, with shear stiffness contributing moderately due to HSDT and transverse matrix modulus being the least influential for the modes. The present model provides an efficient and accurate tool for predicting the vibration behavior of advanced annular disk structures.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3010731

DOI: 10.1155/jom/3010731

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