TY - JOUR
T1 - Chebyshev-Lagrange Multipliers Technique for Vibration Analysis of Functionally Graded Material Beams Using Various Beam Theories
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 - <p style="text-align: justify;">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&#39; 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.</p>