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

Abstract

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.

Folded sheet resonators that aim at low frequency attenuation of surface elastic waves in solids

“…Among the three types of waves, namely, the body torsional waves, the Rayleigh waves, and Love waves, the body waves decay quickly over distance so the total area of severe damage caused by the body waves is much smaller than the Rayleigh and the Love waves, which are surface waves. [31][32][33][34][35] Between the Rayleigh waves that reside in thick soil and the Love waves that reside in shallow soil above bed rock, the Rayleigh waves are more often encountered than Love waves because in geology thick soil cites are more common than shallow soil. Furthermore, once the means to attenuate Rayleigh waves are established, they could serve as a reference for the Love waves.…”

On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

“…In the area of structures and materials, wave propagation-based tools have found increasing applications, especially in structural health monitoring and active control of vibrations and noise (Achenbach, 1973). Regarding the analysis of traveling plane waves across structures consisting of piezoelectric and FGM elements, there are several studies in the literature (Abad and Rouzegar, 2019; Berezovski et al, 2003; Chaudhary et al, 2017, 2018, 2019; Eskandari and Shodja, 2008; Nirwal et al, 2019; Qian et al, 2008; Sahu et al, 2018; Saroj et al, 2019; Singh et al, 2018; Singhal and Sahu, 2017; Singhal et al, 2018a, 2018b, 2019a, 2019b). As notable examples, Singhal et al (2018a, 2018b) used Wentzel-Kramers-Brillouin (WKB) and Liouville-Green (LG) analytical approaches to study surface waves in piezoelectric composite structures.…”

Propagation of Pore Pressure and Stress in Saturated Porous Media Based on a Darcy-Brinkman Formulation

“…Different investigations are available in literature focusing on the mechanical behaviors of piezoelectric nanostructures [3,4] on fields of linear and nonlinear, longitudinal and transverse, free and forced wave propagation in microscale. Initial and couple stress influence on transmission of the Love-type wave [5], and Rayleigh waves [6] in material layers with imperfect interface [7], and surface wave propagation between viscous liquid and initially stressed piezoelectric half-space [8] are investigated by using the spatial varying WKB (Wentzel-Kramers-Brillouin) method [9,10]. Solutions are obtained by a perturbation technique in closed-form for normal, shear stresses, dielectric displacement, and electric potential [11], and it is found that the complex phase velocity with positive imaginary part increases with time [12].…”