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Volume 14, Issue 4
Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories

Sacharuck Pornpeerakeat & Sakda Katawaethwarag

Adv. Appl. Math. Mech., 14 (2022), pp. 871-892.

Published online: 2022-04

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  • 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.

  • AMS Subject Headings

41A50, 65D15, 65D20, 74H45

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COPYRIGHT: © Global Science Press

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@Article{AAMM-14-871, author = {Sacharuck Pornpeerakeat and Sakda Katawaethwarag}, title = {Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0301}, url = {http://global-sci.org/intro/article_detail/aamm/20438.html} }
TY - JOUR T1 - Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories AU - Sacharuck Pornpeerakeat & Sakda Katawaethwarag JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 871 EP - 892 PY - 2022 DA - 2022/04 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0301 UR - https://global-sci.org/intro/article_detail/aamm/20438.html KW - Chebyshev polynomials, Lagrange multipliers, functionally graded material, orthogonality, vibration analysis. AB -

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.

Sacharuck Pornpeerakeat and Sakda Katawaethwarag. (2022). Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories. Advances in Applied Mathematics and Mechanics. 14 (4). 871-892. doi:10.4208/aamm.OA-2020-0301
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