Antiplane Crack Problem in Functionally Graded Piezoelectric Materials

2002 ◽  
Vol 69 (4) ◽  
pp. 481-488 ◽  
Author(s):  
Chunyu Li ◽  
G. J. Weng
Keyword(s):  
Integral Equations ◽  
Piezoelectric Material ◽  
Electric Fields ◽  
Crack Problem ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Functionally Graded Piezoelectric Material ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

In this paper the problem of a finite crack in a strip of functionally graded piezoelectric material (FGPM) is studied. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric permitivity of the FGPM vary continuously along the thickness of the strip, and that the strip is under an antiplane mechanical loading and in-plane electric loading. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. The near-tip singular stress and electric fields are obtained from the asymptotic expansion of the stresses and electric fields around the crack tip. It is found that the singular stresses and electric displacements at the tip of the crack in the functionally graded piezoelectric material carry the same forms as those in a homogeneous piezoelectric material but that the magnitudes of the intensity factors are dependent upon the gradient of the FGPM properties. The investigation on the influences of the FGPM graded properties shows that an increase in the gradient of the material properties can reduce the magnitude of the stress intensity factor.

Scattering of anti-plane shear waves by an interface crack between two bonded dissimilar functionally graded piezoelectric materials

2009 ◽  
Vol 465 (2104) ◽  
pp. 1249-1269 ◽  
Author(s):  
B.M Singh ◽  
J Rokne ◽  
R.S Dhaliwal ◽  
J Vrbik
Keyword(s):  
Integral Equations ◽  
Integral Transform ◽  
Piezoelectric Materials ◽  
Mass Density ◽  
Electric Displacement ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

In the present paper, the dynamic behaviour of a Griffith crack situated at the interface of two bonded dissimilar functionally graded piezoelectric materials (FGPMs) is considered. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPMs vary continuously as an exponential function of the x and y coordinates, and that the FGPMs are under anti-plane mechanical loading and in-plane electrical loading. By using an integral transform technique the problem is reduced to four pairs of dual integral equations, which are transformed into four simultaneous Fredholm integral equations with four unknown functions. By solving the four simultaneous Fredholm integral equations numerically the effects of the material properties on the stress and electric displacement intensity factors are calculated and displayed graphically.

A Mode III Crack in a Functionally Graded Piezoelectric Material Strip

2004 ◽  
Vol 71 (3) ◽  
pp. 327-333 ◽  
Author(s):  
B. L. Wang ◽  
X. H. Zhang
Keyword(s):  
Piezoelectric Material ◽  
Electric Displacement ◽  
Crack Problem ◽  
Functionally Graded ◽  
Mode Iii ◽  
Functionally Graded Piezoelectric Material ◽  
Mode Iii Crack ◽  
Crack Location ◽  
Functional Forms ◽  
Functionally Graded Piezoelectric

This paper considers a mode III crack problem for a functionally graded piezoelectric material strip. The mechanical and electrical properties of the strip are considered for a class of functional forms for which the equilibrium equation has an analytical solution. The problem is solved by means of singular integral equation technique. Both a single crack and two collinear cracks are investigated. The results are tabulated and plotted to show the effect of the material nonhomogeneity and crack location on the stress and electric displacement intensity factors.

Anti-Plane Moving Crack in Functionally Graded Piezoelectric Materials

2002 ◽  
Author(s):  
Bo Jin
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Equations ◽  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Dual Integral Equations ◽  
Moving Crack ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

This paper considers the anti-plane moving crack in functionally graded piezoelectric materials (FGPM). The governing equations for FGPM are solved by means of Fourier cosine transform. The mathematical formulation for the permeable crack condition is derived as a system of dual integral equations. By appropriate transformations, it is shown that the dual integral equations can be reduced to a Fredholm integral equation of the second kind. The results obtained indicate that the stress intensity factor of moving crack in FGPM depends only on the mechanical loading. The gradient parameter of the FGPM and the moving velocity of the crack do have significant influence on the dynamic stress intensity factor.

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.

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.

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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