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

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.

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

Polynomial Approach Modeling of Resonator Piezoelectric Disc

2011 ◽  
Vol 482 ◽  
pp. 11-20 ◽  
Author(s):  
L. Elmaimouni ◽  
J.E. Lefebvre ◽  
F.E. Ratolojanahary ◽  
A. Raherison ◽  
B. Bahani ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Legendre Polynomial ◽  
Electromechanical Coupling ◽  
Three Dimensional ◽  
Electromechanical Coupling Coefficient ◽  
Polynomial Method ◽  
Three Dimensional Modeling ◽  
Wave Resonator ◽  
Piezoelectric Disc ◽  
Harmonic Analyses

Legendre polynomial method which describes the structure and incorporates automatically the boundary conditions in constitutive and propagation equations is used to model acoustic wave cylindrical resonators. It is the first time this method is applied to study standing rather than propagative waves. The advantage of this approach is, in a unique formulation, to take into account electric sources. The analytical and numerical resolutions are presented to highlight the potentialities of the Legendre polynomial approach. The vibration characteristics of piezoelectric discs with regard to diameter to thickness D/H ratios are analyzed by the three dimensional modeling approach through both modal and harmonic analyses. Resonance and antiresonance frequencies, electric input impedance, dispersion curves, field profiles and electromechanical coupling coefficient, easily obtained, are presented for PZT5A resonator piezoelectric discs. To validate our approach, the results using our 3D polynomial modelling of acoustic wave resonator are compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the radial modes of all orders.

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