Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories

Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories

Year:    2022

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 871–892

Abstract

In this paper, a new technique for analysing functionally graded material (FGM) beams using the Chebyshev polynomials and Lagrange multipliers with various beam theories is presented. By utilizing the inner products and the Chebyshev polynomials' orthogonality properties incorporated with Lagrange multipliers, we can combine the governing equation and boundary conditions to yield the matrix equations with explicit weighting coefficients. Numerical examples are provided for vibration analysis of various beam theories and assumptions. Based on numerical evaluations, it is revealed that the proposed technique can efficiently achieve good agreement with those of the references.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2020-0301

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 871–892

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Chebyshev polynomials Lagrange multipliers functionally graded material orthogonality vibration analysis.

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