Guided waves in multilayered hollow cylinders: The improved Legendre polynomial method

2013 ◽  
Vol 95 ◽  
pp. 419-429 ◽  
Author(s):  
J.G. Yu ◽  
J.E. Lefebvre
Keyword(s):  
Legendre Polynomial ◽  
Guided Waves ◽  
Polynomial Method ◽  
Hollow Cylinders

scholarly journals A Recursive Legendre Polynomial Analytical Integral Method for the Fast and Efficient Modelling Guided Wave Propagation in Rectangular Section Bars of Orthotropic Materials

2021 ◽  
Vol 26 (3) ◽  
pp. 221-230
Author(s):  
Xiaoming Zhang ◽  
Shuangshuang Shao ◽  
Shuijun Shao
Keyword(s):  
Numerical Integration ◽  
Legendre Polynomial ◽  
Guided Waves ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Orthotropic Materials ◽  
Polynomial Method

Ultrasonic guided waves are widely used in non-destructive testing (NDT), and complete guided wave dispersion, including propagating and evanescent modes in a given waveguide, is essential for NDT. Compared with an infinite plate, the finite lateral width of a rectangular bar introduces a greater density of modes, and the dispersion solutions become more complicated. In this study, a recursive Legendre polynomial analytical integral (RLPAI) method is presented to calculate the dispersion behaviours of guided waves in rectangular bars of orthotropic materials. The existing polynomial method involves a large number of numerical integration steps, and it is often computationally costly to compute these integrals. The presented RLPAI method uses analytical integration instead of numerical integration, thus leading to a significant improvement in the computational speed. The results are compared with those published previously to validate our method, and the computational efficiency is discussed. The full three-dimensional dispersion curves are plotted. The dispersion characteristics of propagating and evanescent waves are investigated in various rectangular bars. The influences of different width-to-thickness ratios on the dispersion curves of four types of low-order modes for a rectangular bar of an orthotropic composite are illustrated.

scholarly journals Modelling guided waves in anisotropic plates using the Legendre polynomial method

2017 ◽  
Vol 104 ◽  
pp. 02015
Author(s):  
Mingfang Zheng ◽  
Cunfu He ◽  
Yan Lu ◽  
Bin Wu
Keyword(s):  
Legendre Polynomial ◽  
Guided Waves ◽  
Polynomial Method ◽  
Anisotropic Plates

Investigation of guided waves propagation in orthotropic viscoelastic carbon–epoxy plate by Legendre polynomial method

2016 ◽  
Vol 74 ◽  
pp. 27-33 ◽  
Author(s):  
Cherif Othmani ◽  
Souhail Dahmen ◽  
Anouar Njeh ◽  
Mohamed Hédi Ben Ghozlen
Keyword(s):  
Legendre Polynomial ◽  
Guided Waves ◽  
Polynomial Method ◽  
Waves Propagation

Guided Waves in Hollow Cylinders: Theoretical and Numerical Study

2021 ◽  
pp. 295-303
Author(s):  
Quang Hung Le ◽  
Yen Nguyen ◽  
Hoai Nguyen ◽  
Duy Kien Dao ◽  
Hoai-Nam Tran ◽  
...  
Keyword(s):  
Guided Waves ◽  
Numerical Study ◽  
Hollow Cylinders

Viscoelastic Circumferential SH Wave in Graded Hollow Cylinders

2014 ◽  
Vol 543-547 ◽  
pp. 7-11
Author(s):  
X.D. Yang ◽  
J.G. Yu
Keyword(s):  
Wave Propagation ◽  
Nondestructive Evaluation ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Polynomial Method ◽  
Sh Wave ◽  
Graded Material ◽  
Viscoelastic Theory ◽  
Hollow Cylinders ◽  
Dispersion And Attenuation

In this article, circumferential SH wave propagation in functionally graded material (FGM) hollow cylinders is investigated. Based on the Kelvin-Voigt viscoelastic theory, the controlling differential equations in terms of displacements are deduced. By the Legendre polynomial method, the asymptotic solutions are obtained. Through the numerical results, the influences of gradient profile and the influences of the radius to thickness ratio on dispersion and attenuation are illustrated. The work is crucial for guided ultrasonic nondestructive evaluation for graded hollow cylinders.

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