Circumferential thermoelastic Lamb wave in fractional order cylindrical plates

Abstract

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.

An analytical integration Legendre polynomial series approach for Lamb waves in fractional order thermoelastic multilayered plates

“…Then the analytical expression is deduced based on the orthogonality of Legendre polynomial for each type and used to improve the computational efficiency. The efficiency of the analytical integration on time‐consuming problems has been verified in references 27,28 . In reference, 27 the analytical expressions are developed for functionally graded structures based on the series expansion form of Legendre polynomial.…”

“…The efficiency of the analytical integration on time-consuming problems has been verified in references. 27,28 In reference, 27 the analytical expressions are developed for functionally graded structures based on the series expansion form of Legendre polynomial. In reference, 28 the analytical expressions are developed for uniform hollow cylinder mainly based on the iterative calculations.…”

“…27,28 In reference, 27 the analytical expressions are developed for functionally graded structures based on the series expansion form of Legendre polynomial. In reference, 28 the analytical expressions are developed for uniform hollow cylinder mainly based on the iterative calculations. In this paper, based on the orthogonality of Legendre polynomial, the analytical integrals are given in more concise form for multilayered plates to avoid the numerical error accumulation problem in treating higher order Legendre polynomials in the iterative calculations.…”

Nonlocal elasticity and thermal dual‐phase‐lag effect on the vibration analysis of transversely isotropic electro‐magneto generalized thermoelastic sphere with voids

“…Sharma and Mishra [51] studied the vibration analysis of non-homogeneous thermoelastic sphere with traction free boundary conditions. Lots of work for free and forced vibrations in the reference of homogeneous and inhomogeneous materials were done by some researchers and authors such as Sharma et al [52], Abbas [53], Sharma and Mittal [54], Wang et al [55], Sharma et al [56], etc.…”