scholarly journals Computation of Propagating and Non-Propagating Lamb-Like Wave in a Functionally Graded Piezoelectric Spherical Curved Plate by an Orthogonal Function Technique

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2363 ◽  
Author(s):  
Xiaoming Zhang ◽  
Shunli Liang ◽  
Xiaoming Han ◽  
Zhi Li
Keyword(s):  
Dispersion Equation ◽  
Acoustic Waves ◽  
Guided Wave ◽  
Functionally Graded ◽  
Wave Number ◽  
Function Technique ◽  
Orthogonal Function ◽  
Propagating Waves ◽  
Complex Wave ◽  
Functionally Graded Piezoelectric

Non-propagating waves have great potential for crack evaluation, but it is difficult to obtain the complex solutions of the transcendental dispersion equation corresponding to the non-propagating wave. This paper presents an analytical approach based on the orthogonal function technique to investigate non-propagating Lamb-like waves in a functionally graded piezoelectric spherical curved plate. The presented approach can transform the set of partial differential equations for the acoustic waves into an eigenvalue problem that can give the generally complex wave numbers and the field profiles. A comparison of the obtained results with the well-known ones in plates is provided. The obtained solutions of the dispersion equation are shown graphically in three dimensional frequency-complex wave number space, which aids in understanding the properties of non-propagating waves better. The properties of the guided wave, including real, purely imaginary, and complex branches in various functionally graded piezoelectric spherical curved plates, are studied. The effects of material piezoelectricity, graded fields, and mechanical and electrical boundary conditions on the dispersion characteristics, are illustrated. The amplitude distributions of displacement and electric potential are also discussed, to analyze the specificities of non-propagating waves.

scholarly journals The Complex Rayleigh Waves in a Functionally Graded Piezoelectric Half-Space: An Improvement of the Laguerre Polynomial Approach

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2320 ◽  
Author(s):  
Ke Li ◽  
Shuangxi Jing ◽  
Jiangong Yu ◽  
Xiaoming Zhang ◽  
Bo Zhang
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Wave Mode ◽  
Functionally Graded ◽  
Function Technique ◽  
Complex Wave ◽  
Acoustic Wave Devices ◽  
Functionally Graded Piezoelectric

The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.

Full dispersion and characteristics of complex guided waves in functionally graded piezoelectric plates

2019 ◽  
Vol 30 (10) ◽  
pp. 1466-1480 ◽  
Author(s):  
Xiaoming Zhang ◽  
Chuanzeng Zhang ◽  
Jiangong Yu ◽  
Jing Luo
Keyword(s):  
Evanescent Wave ◽  
Guided Waves ◽  
Electromechanical Coupling ◽  
Phase Speed ◽  
Evanescent Waves ◽  
Guided Wave ◽  
Functionally Graded ◽  
Function Technique ◽  
Functionally Graded Piezoelectric ◽  
Piezoelectric Plates

The improvement of the resolution and energy conversion efficiency of piezoelectric devices requires a thorough study of guided wave, especially the evanescent wave modes with high-phase speed and low attenuation. Due to the computation difficulties, investigations about the evanescent wave in piezoelectric structures are rather limited. In this article, an analytic method based on the orthogonal function technique is presented to investigate the complex dispersion relations and the evanescent guided wave in functionally graded piezoelectric plates, which can convert the complex partial differential equations with variable coefficients into an eigenvalue problem and obtain all solutions. Comparisons with other related studies are conducted to validate the correctness of the presented method. Three-dimensional full dispersion curves are plotted to gain a better insight into the nature of the evanescent waves. The influences of piezoelectricity and graded fields and electrical boundary conditions on evanescent waves are illustrated. The electromechanical coupling factors of the functionally graded piezoelectric material plates with different gradient fields are also investigated. Furthermore, the displacement amplitude and electric potential distributions are also discussed to illustrate the specificities of evanescent guided waves. The corresponding results presented in this work are promised to be used to improve the resolution of piezoelectric transducers.

Approximation of surface wave velocity in smart composite structure using Wentzel–Kramers–Brillouin method

2018 ◽  
Vol 29 (18) ◽  
pp. 3582-3597 ◽  
Author(s):  
Manoj Kumar Singh ◽  
Sanjeev A Sahu ◽  
Abhinav Singhal ◽  
Soniya Chaudhary
Keyword(s):  
Surface Wave ◽  
Piezoelectric Material ◽  
Half Space ◽  
Composite Structure ◽  
Functionally Graded ◽  
Wave Number ◽  
Practical Utilization ◽  
Functionally Graded Piezoelectric Material ◽  
Varying Coefficients ◽  
Functionally Graded Piezoelectric

In mathematical physics, the Wentzel–Kramers–Brillouin approximation or Wentzel–Kramers–Brillouin method is a technique for finding approximate solutions to linear differential equations with spatially varying coefficients. An attempt has been made to approximate the velocity of surface seismic wave in a piezo-composite structure. In particular, this article studies the dispersion behaviour of Love-type seismic waves in functionally graded piezoelectric material layer bonded between initially stressed piezoelectric layer and pre-stressed piezoelectric half-space. In functionally graded piezoelectric material stratum, theoretical derivations are obtained by the Wentzel–Kramers–Brillouin method where variations in material gradient are taken exponentially. In the upper layer and lower half-space, the displacement components are obtained by employing separation of variables method. Dispersion equations are obtained for both electrically open and short cases. Numerical example and graphical manifestation have been provided to illustrate the effect of influencing parameters on the phase velocity of considered surface wave. Obtained relation has been deduced to some existing results, as particular case of this study. Variation in cut-off frequency and group velocity against the wave number are shown graphically. This study provides a theoretical basis and practical utilization for the development and construction of surface acoustics wave devices.

scholarly journals Analysis of wave propagation in cylinders and rods made of functionally graded piezoelectric material

2019 ◽  
Author(s):  
Andrey Blinov
Keyword(s):  
Piezoelectric Material ◽  
Phase Speed ◽  
Guided Wave ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Piezoelectric Material ◽  
Design And Optimization ◽  
Points Of View ◽  
Functionally Graded Piezoelectric ◽  
Piezoelectric Constants

In this paper we study from both theoretical and numerical points of view the problem of design and optimization of functionally graded piezoelectric material (FGPM) transducers. The governing equations for FGPM are solved using numerical scheme based on the polynomial approach. The lowest frequencies for circular and rectangular rings with different radius-to-thickness ratios are calculated to study the guided wave characteristics. It is assumed that elastic stiffnesses,piezoelectric constants and dielectric permitivities of FGPM vary in an arbitrary way inside a structure. The fundamental mode starts propagating at the phase speed that is determined numerically. Finally, two-dimensional numerical simulations are performed for various parameters to control the accuracy of the solution.

scholarly journals Complex dispersion solutions for guided waves and properties of non-propagating waves in a piezoelectric spherical plate

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401882069
Author(s):  
Xiaoming Zhang ◽  
Zhi Li ◽  
Jiangong Yu
Keyword(s):  
Guided Waves ◽  
Three Dimensional ◽  
Guided Wave ◽  
Wave Number ◽  
Polynomial Method ◽  
Propagating Waves ◽  
Complex Solutions ◽  
Spherical Plate ◽  
Complex Valued ◽  
Dispersion And Attenuation

The vibration modes of an elastic plate are usually divided into propagating and non-propagating (evanescent) kinds. Non-propagating wave modes are very important for guided wave inspection of defect size and shape. But it is difficult to obtain the complex solutions of the transcendental dispersion equation, corresponding to the non-propagating wave. In this article, we present an improved Legendre polynomial method to calculate the complex-valued dispersion and study properties of the non-propagating wave in a piezoelectric spherical plate. Comparisons with other related studies are conducted to validate the correctness of the presented method. The complete dispersion and attenuation curves are plotted in three-dimensional frequency-complex wave number space. The influences of material piezoelectricity and radius–thickness ratio on non-propagating waves in piezoelectric spherical plates are investigated. The amplitude distributions of the electric potential and displacement are also discussed in detail. All the results presented in this work can provide theoretical guidance for ultrasonic nondestructive evaluation and are promising to be applied to improve the resolution of piezoelectric transducers.

Effect of interfacial imperfection on shear wave propagation in a piezoelectric composite structure: Wentzel–Kramers–Brillouin asymptotic approach

2019 ◽  
Vol 30 (18-19) ◽  
pp. 2789-2807 ◽  
Author(s):  
Pulkit Kumar ◽  
Moumita Mahanty ◽  
Amares Chattopadhyay ◽  
Abhishek Kumar Singh
Keyword(s):  
Piezoelectric Material ◽  
Half Space ◽  
Composite Structure ◽  
Functionally Graded ◽  
Wave Number ◽  
Piezoelectric Composite ◽  
Sh Wave ◽  
Functionally Graded Piezoelectric Material ◽  
Material Layer ◽  
Functionally Graded Piezoelectric

The primary objective of this article is to investigate the behaviour of horizontally polarized shear (SH) wave propagation in piezoelectric composite structure consisting of functionally graded piezoelectric material layer imperfectly bonded to functionally graded porous piezoelectric material half-space. The linear form of functional gradedness varying continuously along with depth is considered in both functionally graded piezoelectric material layer and functionally graded porous piezoelectric material half-space. The interface of the composite structure is considered to be damaged mechanically and/or electrically. Wentzel–Kramers–Brillouin asymptotic approach is adopted to solve the coupled electromechanical field differential equations of both functionally graded piezoelectric material layer and functionally graded porous piezoelectric material half-space. An analytical treatment has been employed to determine the dispersion relations of propagating SH-wave for both electrically short and electrically open conditions, which further reduced to the pre-established and classical results as special case of the problem. The effect of various affecting parameters, namely, functional gradedness, wave number, mechanical/electrical imperfection parameters in the presence and absence of porosity on the phase velocity of SH-wave, has been reported through numerical computation and graphical demonstration. In addition, the variation of the coupled electromechanical factor with dimensionless wave number and cut-off frequency with different modes of propagation of wave for electrically short and electrically open cases has also been discussed.

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