Modelling of Love Waves in a Heterogeneous Medium Demarcated by Functionally Graded Piezoelectric Layer and Size-Dependent Micropolar Half-Space

2021 ◽  
Author(s):  
Prasenjit Pati ◽  
Shishir Gupta
Keyword(s):  
Half Space ◽  
Piezoelectric Layer ◽  
Heterogeneous Medium ◽  
Functionally Graded ◽  
Love Waves ◽  
Size Dependent ◽  
Functionally Graded Piezoelectric

scholarly journals Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

2015 ◽  
Vol 40 (2) ◽  
pp. 273-281 ◽  
Author(s):  
Piotr Kiełczyński ◽  
Marek Szalewski ◽  
Andrzej Balcerzak ◽  
Krzysztof Wieja
Keyword(s):  
Group Velocity ◽  
Half Space ◽  
Functionally Graded Materials ◽  
Integral Formula ◽  
Liouville Problem ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials ◽  
Sturm Liouville

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

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 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.

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