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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