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**Wave propagation in thermoelastic inhomogeneous hollow cylinders by analytical integration orthogonal polynomial approach.**
*(English)*
Zbl 1481.74382

Summary: A new solving procedure based on the Legendre polynomial series is developed to investigate the longitudinal guided waves in fractional order thermoelastic inhomogeneous hollow cylinders. Different from the available Legendre polynomial approach, integrals are calculated by the explicit and simple expressions to replace the numerical solutions. The solutions according to the global matrix method (GMM) are also derived for the first time to verify the effectiveness of the presented approach. Comparison of the CPU time indicates that the computational efficiency of the new solving procedure has a huge improvement. Then, the guided wave phase velocity dispersion curves, attenuation curves, displacement and temperature distributions for functionally graded hollow cylinders with different fractional orders, flexural orders, radius-thickness ratios and gradient fields are analyzed. It is found that the attenuation coefficients of flexural longitudinal modes rapidly decrease when the flexural torsional mode curve is close to the flexural longitudinal mode curve. Furthermore, notable influence of the flexural order on attenuation curves mainly occurs at the cut-off frequencies and mutation frequencies. In addition, a smaller radius-thickness ratio implies a larger attenuation, and the temperature amplitudes of flexural torsional mode are more and more close to those of longitudinal mode when the radius-thickness ratio decreases.

### MSC:

74J05 | Linear waves in solid mechanics |

35Q74 | PDEs in connection with mechanics of deformable solids |

### Keywords:

thermoelastic guided wave; analytical integral; Legendre polynomial; fractional order; hollow cylinder; attenuation
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\textit{X. Wang} et al., Appl. Math. Modelling 99, 57--80 (2021; Zbl 1481.74382)

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