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Circumferential thermoelastic Lamb wave in fractional order cylindrical plates
Author(s) -
Wang Xianhui,
Li Fanglin,
Yu Jiangong,
Zhang Xiaoming,
Li Zhi
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000208
Subject(s) - thermoelastic damping , legendre polynomials , orthotropic material , mathematical analysis , amplitude , eigenvalues and eigenvectors , fractional calculus , mathematics , radius , polynomial , physics , thermal , optics , thermodynamics , finite element method , quantum mechanics , computer security , computer science
An improved Legendre polynomial series approach (AILPSA) is presented to investigate the circumferential thermoelastic Lamb wave in a fractional order orthotropic cylindrical plate. In the AILPSA, the analytical integration is developed based on the orthogonality and recursive properties of the Legendre polynomial to simplify the integral computation involved in the solving progress. As a consequence, the computational efficiency is improved significantly. Results are compared with those from the previous article to confirm the validity of the introduced method. Using the AILPSA, guided wave characteristics in various fractional order orthotropic cylindrical plates are investigated by solving the eigenvalues and eigenvectors of the system of algebraic equations. The influences of fractional order and radius‐thickness ratio on dispersion curve and displacement, temperature amplitudes are illustrated. The results show that the fractional order almost has no effect on the phase velocities of quasi‐elastic wave modes, but has notable effect on their attenuations. A smaller fractional order means a smaller temperature amplitude for the quasi‐elastic wave mode, but means a larger temperature amplitude for the thermal wave mode. A smaller radius thickness ratio indicates a smaller attenuation and a larger temperature amplitude.