scholarly journals Modelling guided waves in layered media materials using the state-vector formalism and legendre polynomial method

2017 ◽  
Author(s):  
Yan Lyu ◽  
Jie Gao ◽  
Guorong Song ◽  
Cunfu He ◽  
Bin Wu
Keyword(s):  
Legendre Polynomial ◽  
State Vector ◽  
Guided Waves ◽  
Layered Media ◽  
The State ◽  
Polynomial Method

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

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

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