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.

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.

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.

Analysis of gravity and non-homogeneity on Rayleigh wave in anisotropic elastic-viscoelastic half space of higher order

2015 ◽  
Vol 11 (1) ◽  
pp. 120-130 ◽  
Author(s):  
Rajneesh Kakar
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Mass Density ◽  
Wave Number ◽  
Inhomogeneous Layer ◽  
Third Order ◽  
Content Type ◽  
Anisotropic Elastic ◽  
Mathematical Techniques

Purpose – The purpose of this paper is to illustrate the propagation of Rayleigh waves in an anisotropic inhomogeneous layer placed over an isotropic gravitational viscoelastic half space of third order. Design/methodology/approach – It is considered that the mass density and the elastic coefficients of the layer are space dependent. Dispersion properties of waves are derived with the simple mathematical techniques. Graphs are plotted between phase velocity ‘k’ and wave number ‘c’ for different values of inhomogeneity parameters for a particular model and the effects of inhomogeneity and gravity are studied. Findings – The wave analysis indicates that the phase velocity of Rayleigh waves is affected quite remarkably by the presence of inhomogeneity, gravity and strain rates of strain parameters in the half space. The effects of inhomogeneity and depth on the phase velocity are also shown in corresponding figures. Originality/value – The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists.

Propagation of Cylindrical Rayleigh Waves in a Transversly Isotropic Thermoelastic Diffusive Solid Half-Space

2013 ◽  
Vol 43 (3) ◽  
pp. 3-20 ◽  
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Phase Velocity ◽  
Boundary Conditions ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Attenuation Coefficients ◽  
Special Cases ◽  
Phase Velocity And Attenuation

Abstract The propagation of cylindrical Rayleigh waves in a trans- versely isotropic thermoelastic diffusive solid half-space subjected to stress free, isothermal/insulated and impermeable or isoconcentrated boundary conditions is investigated in the framework of different theories of ther- moelastic diffusion. The dispersion equation of cylindrical Rayleigh waves has been derived. The phase velocity and attenuation coefficients have been computed from the dispersion equation by using Muller’s method. Some special cases of dispersion equation are also deduced

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