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.

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.

On point source influencing Love-type wave propagation in a functionally graded piezoelectric composite structure: A Green’s function approach

2018 ◽  
Vol 29 (9) ◽  
pp. 1928-1940 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
Amrita Das ◽  
Anusree Ray ◽  
Amares Chattopadhyay
Keyword(s):  
Green’S Function ◽  
Piezoelectric Material ◽  
Half Space ◽  
Green's Function ◽  
Composite Structure ◽  
Functionally Graded ◽  
Functionally Graded Piezoelectric Material ◽  
Material Layer ◽  
Type Wave ◽  
Functionally Graded Piezoelectric

Green’s function plays an important role in solving the problems concerning point action or impulse responsible for wave motions in materials. Prime objective of the this article is to investigate the propagation behaviour of Love-type wave influenced by a point source in a composite structure comprising a functionally graded piezoelectric material layer lying over a functionally graded fibre-reinforced material half-space. Green’s function technique is adopted in order to obtain the dispersion equation, which is further reduced to the classical Love wave equation as a particular case of the problem. The effect of increasing thickness of functionally graded piezoelectric material layer on the circular frequency and wave number is unravelled and depicted graphically. Moreover, influence of heterogeneity, piezoelectricity and dielectric constant associated with functionally graded piezoelectric material layer and effect of heterogeneity parameter and corresponding magnification factor concerned with functional gradedness of functionally graded fibre-reinforced material half-space have been reported through numerical computation and graphical delineation. For sake of computation, numerical data of PZT-5H ceramics for the functionally graded piezoelectric material layer and carbon-fibre epoxy-resin for functionally graded fibre-reinforced material half-space have been considered. Comparative study is performed to elucidate the effect of presence and absence of reinforcement in functionally graded half-space on the phase velocity of Love-type wave propagating in composite structure.

Static bending and dynamic analysis of functionally graded piezoelectric beam subjected to electromechanical loads

2016 ◽  
Vol 230 (19) ◽  
pp. 3457-3469 ◽  
Author(s):  
Vibhuti B Pandey ◽  
Sandeep K Parashar
Keyword(s):  
Piezoelectric Material ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Element Analysis ◽  
Functionally Graded Piezoelectric Material ◽  
Piezoelectric Beam ◽  
Effective Material Properties ◽  
Dimensional Finite Element ◽  
Electromechanical Loading ◽  
Functionally Graded Piezoelectric

This paper investigates the static bending and free vibration analysis of functionally graded piezoelectric material beam under electromechanical loading. The effective material properties of functionally graded piezoelectric material beam are assumed to vary continuously through the thickness direction and are graded according to sigmoid law distribution. Both multi-layered and monomorph models have been considered in the present work. A two-dimensional finite element analysis has been performed using COMSOL Multiphysics® (version 4.2) software. The accuracy of the method was validated by comparing the results with the previous published work. The results presented in the paper shall be useful in the design of functionally graded piezoelectric material beam.

Response analysis of hybrid functionally graded material plate subjected to thermo-electro-mechanical loading

2020 ◽  
pp. 146442072098003
Author(s):  
Pawan Kumar ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Piezoelectric Material ◽  
Functionally Graded Material ◽  
Axial Stress ◽  
Functionally Graded ◽  
Response Analysis ◽  
Functionally Graded Piezoelectric Material ◽  
Graded Material ◽  
Functionally Graded Piezoelectric

Static and free vibration response analysis of a functionally graded piezoelectric material plate under thermal, electric, and mechanical loads is done in this study. The displacement field is acquired using the first-order shear deformation theory, and the Hamilton principle is applied to deduce the motion equations. Temperature-dependent material properties of the functionally graded material plate are used, and these properties follow the power-law distributions along the thickness direction. However, the properties of piezoelectric material layers are assumed to be independent of the electric field and temperature. Finite element formulation for the functionally graded piezoelectric material plate is done using the combined effect of mechanical and electrical loads. The effects of parameters like electrical loading, volume fraction exponent N, and temperature distribution on the static and free vibration characteristics of the functionally graded piezoelectric material square plate are analyzed and presented. Responses are obtained in terms of the centerline deflection, axial stress and the nondimensional natural frequency with various boundary conditions. It is observed that the centerline deflection and nondimensional natural frequency increases as exponent N increases. At the same time, the axial stress decreases with an increase in exponent N. The findings of the static and the free vibration analysis suggest the potential application of the functionally graded piezoelectric material plate in the piezoelectric actuator as well as for sensing deflection in bimorph.

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