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Purpose <p>The computational efficiency of numerical solutions in structural analysis is a critical concern for researchers and scientists. In this work, the&#xa0;author has integrated a parallel computing algorithm and MAPLE within MATLAB to analyse the asymmetric vibrations of multi-directional&#xa0;functionally graded annular nanoplates with linearly varying thickness under thermal environment.</p> Methodology <p>The temperature-dependent material properties and nonlinear temperature profile are assumed to vary in radial and thickness directions. Being functionally graded material, the contribution of the physical neural surface has also been included. The thickness of the plate is assumed to vary linearly in the radial direction. Based on first-order shear deformation theory, Hamilton's principle produced the governing equations that are discretized by the Chebyshev polynomials to compute the fundamental frequencies. Further, the introduction of sizedependency also affects the boundary conditions, particularly, simply-supported boundary conditions have been modified to compute the correct values of fundamental frequencies.</p> Results <p>The adopted approach significantly reduced computational cost by employing the Chebyshev polynomials. The inclusion of MAPLE and parallel computing for symbolic computation drastically decreases the computational cost of the analysis. The investigation of the effect of nonlocal parameter, non-uniformity parameter, graded indexes, temperature profile, and nodal lines on the frequency parameter has also been presented. Silicon Nitride (Si3N4) and Aluminium Alloy (6061-T6Al) are adopted as ceramic and metal, respectively.</p>

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An Investigation for Asymmetric Vibrations of Multi-dimensional Functionally Graded Heated Non-Uniform Annular Nanoplates using Chebyshev Polynomials and Parallel Computing

  • 期刊论文

  • 发表日期：

    2025年5月8日

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  • Rahul Saini

摘要

Purpose

The computational efficiency of numerical solutions in structural analysis is a critical concern for researchers and scientists. In this work, the author has integrated a parallel computing algorithm and MAPLE within MATLAB to analyse the asymmetric vibrations of multi-directional functionally graded annular nanoplates with linearly varying thickness under thermal environment.

Methodology

The temperature-dependent material properties and nonlinear temperature profile are assumed to vary in radial and thickness directions. Being functionally graded material, the contribution of the physical neural surface has also been included. The thickness of the plate is assumed to vary linearly in the radial direction. Based on first-order shear deformation theory, Hamilton's principle produced the governing equations that are discretized by the Chebyshev polynomials to compute the fundamental frequencies. Further, the introduction of sizedependency also affects the boundary conditions, particularly, simply-supported boundary conditions have been modified to compute the correct values of fundamental frequencies.

Results

The adopted approach significantly reduced computational cost by employing the Chebyshev polynomials. The inclusion of MAPLE and parallel computing for symbolic computation drastically decreases the computational cost of the analysis. The investigation of the effect of nonlocal parameter, non-uniformity parameter, graded indexes, temperature profile, and nodal lines on the frequency parameter has also been presented. Silicon Nitride (Si3N4) and Aluminium Alloy (6061-T6Al) are adopted as ceramic and metal, respectively.