08-16-2017, 10:28 PM
Abstract
Bidirectional flexure analysis of functionally graded (FG) plate integratedwith piezoelectric fiber reinforced composites (PFRC) is presented in this paper. A higher order shear and normal deformation theory (HOSNT12) is used to analyze such hybrid or smart FG plate subjected to electromechanical loading. The displacement function of the present model is approximated as Taylor s series in the thickness coordinate, while the electro-static potential is approximated as layer wise linear through the thickness of the PFRC layer. The equations of equilibrium are obtained using principle of minimum potential energy and solution is by Navier s technique. Elastic constants are varying exponentially along thickness (z axis) for FG material while Poisson s ratio is kept constant. PFRC actuator attached either at top or bottomof FGplate and analyzed under mechanical and coupled mechanical and electrical loading. Comparison of present HOSNT12 is made with exact and finite element method (FEM). Keywords Higher order theory _ Piezoelectric fiber reinforced composites _ Functionally Graded
1 Introduction
Piezoelectric materials transform elastic field into the electric field and converse behavior leads many researchers to study their controlling capabilities applicable to structures like plates and shells. Such structures are called as smart, intelligent, adaptive as well as hybrid structures. In conventional composites failure occurs at interface due to abrupt change in material properties. Elastic properties are varying smoothly across the thickness of the FG material and hence failure due to de lamination is avoided. Piezoelectric materials show coupling phenomenon between elastic and electric fields. Tiersten and Mindlin (1962) initiated work on piezoelectric plates. Further Tiersten (1969) contributed this work by exploring the governing equations of linear piezoelectric continuum by analyzing vibrations of a single piezoelectric layer. Monolithic piezoelectric materials exhibit very low stress/strain coefficients and hence low controlling capabilities. Smith and Auld (1991) presented micromechanical analysis of vertically reinforced piezoelectric composites with slight increase in the stress/ strain piezoelectric coefficients. Mallik and Ray (2003) proposed the concept of unidirectional piezoelectric fiber reinforced composite (PFRC) materials and presented their effective elastic and piezoelectric properties. Piezoelectric stress/strain coefficients are improved considerably as compared to monolithic piezoelectric materials.
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