In this article, free vibration studies on functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional (3-D) character of the solution is preserved. The finite element model is derived based on constitutive equation of magneto-electro-elastic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with the isotropic 3-D exact benchmark solutions available in literature. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electrical type of loading on induced magneto-electro-elastic fields. Further study has been carried out on higher harmonic. Study has been extended on functionally graded and layered magneto-electro-elastic plate. © 2006 Elsevier Ltd. All rights reserved.

Rajesh K. Bhangale

Natrajan Ganesan

Anisotropy

Elastic moduli

ELASTICITY

Electric potential

Electromagnetism

finite element method

Magnetic properties

MAGNETO-ELECTRO-ELASTIC FIELDS

MAGNETO-ELECTRO-ELASTIC PLATES

Vibrations (mechanical)

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Journal of Sound and Vibration

Free vibration response of functionally graded (FG) elastic, rectangular, and simply (diaphragm) supported plates is presented based on higher order shear/shear-normal deformations theories (HOSTs/HOSNTs). The theoretical models are based on Taylor's series expansion of in-plane and transverse displacements in thickness coordinate defining the plate deformations. Some of these advanced models account for the effects of transverse shear deformations, transverse normal deformation and non-linear variation of in-plane displacements through plate's thickness. Functionally graded materials (FGMs) are idealized as continua with mechanical properties changing smoothly with respect to spatial coordinates. The material properties of FG plates are assumed here to be varying through thickness of plate in a continuous manner. Poisson's ratios of FG plates are assumed constant, but their Young's modulii and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as exponential and power law functions. The equations of motion are derived using Hamilton's principle on the basis of HOSTs/HOSNTs. Numerical solutions are obtained using Navier solution method. The accuracy of numerical solutions is first established through comparison with the exact three dimensional (3D) elasticity solutions and then compared with available other models' solutions. New solutions are then provided for future use. © 2012 Elsevier Ltd.

Composite Structures

Free vibration response of functionally graded thick plates with shear and normal deformations effects

In view of the significant increase in research activity and publications in functionally graded materials (FGMs) and structures in the last few years, the present article is an attempt to identify and highlight the topics that are most relevant to FGMs and structures and review representative journal publications that are related to those topics. A critical review of the reported studies in the area of thermo-elastic and vibration analyses of functionally graded (FG) plates with an emphasis on the recent works published since 1998. Because of the extensive growth in the body of knowledge in FGMs in the last two decades, it is prudent to reduce the review to a manageable level by concentrating on the FG plate problems only. The review carried out here, is concerned with deformation, stress, vibration and stability problems of FG plates. This review is intended to give the readers a feel for the variety of studies and applications related to graded composites. An effort has been made here, to include all the important contributions in the current area of interest. The critical areas regarding future research needs for the successful implementation of FGM in design are outlined in the conclusions. © 2012 Elsevier Ltd.

A critical review of recent research on functionally graded plates

Studies on functionally graded magneto-electro-elastic cylindrical shells have been carried out in the present work by using semi-analytical finite element formulation. The finite element model is derived based on constitutive equation of piezomagnetic material accounting for coupling between elasticity, electric and magnetic effect. The functionally graded model similar to conventional functionally graded material in literature has been adopted. Studies are carried out on clamped-clamped shell and frequency behavior with the variation of power law index is analyzed and explained on the basis of constitutive material.

International Journal of Computational Methods in Engineering Science and Mechanics

Free vibration of functionally graded non-homogeneous magneto-electro- elastic cylindrical shell

In recent years, structures made up of functionally graded materials (FGMs) have received considerable attention for use in high-temperature applications. In this article, a finite element formulation based on First-Order Shear Deformation Theory (FSDT) is used to study the thermal buckling and vibration behavior of truncated FGM conical shells in a high-temperature environment. A Fourier series expansion for the displacement variable in the circumferential direction is used to model the FGM conical shell. The material properties of the truncated FGM conical shells are functionally graded in the thickness direction according to a volume fraction power law distribution. Temperature-dependent material properties are considered to carry out a linear thermal buckling and free vibration analysis. The conical shell is assumed to be clamped-clamped and has a high temperature specified on the inner surface while the outer surface is at ambient temperature. The one-dimensional heat conduction equation is used across the thickness of the conical shell to determine the temperature distribution and thereby the material properties. In addition, the influence of initial stresses on the frequency behavior of FGM shells has also been investigated. Numerical studies involving the understanding of the role of power law index, r/h ratios, and semi-vertex angle on the thermal buckling temperature as well as on vibration have been carried out. © 2005 Elsevier Ltd. All rights reserved.

Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells

In this article, static analysis of functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional character of the solution is preserved. The finite element model is derived based on constitutive equation of piezomagnetic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The other fields are calculated by post-computation through constitutive equation. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with available functionally graded three-dimensional exact benchmark solutions given by Pan and Han [Pan, E., Han, F., in press. Green's function for transversely isotropic piezoelectric functionally graded multilayered half spaces. Int. J. Solids Struct.]. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electric type of loading on induced magneto-electro-elastic fields. In addition further study has been carried out on non-homogeneous transversely isotropic FGM magneto-electro-elastic plate available in the literature [Chen, W.Q., Lee, K.Y., Ding, H.J., 2005. On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates].

Fulltext

International Journal of Solids and Structures

Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates

In this article, free vibration studies on Functionally Graded Materials (FGM) magneto-electro-elastic cylindrical shells have been carried out. A series solution is assumed in circumferential and axial direction such that the three-dimensional character of the solution is preserved. The finite element model is derived based on constitutive equation of magneto-electro-elastic material accounting for coupling between elasticity, electric and magnetic effect. Frequency behavior with the variation of power law index is analyzed and explained on the basis of constitutive material. One of the aims of the study is to evaluate the influence of magnetic and piezoelectric effect on the structural frequency. In addition influence of length to radius ratio and radius to thickness ratio on the frequency behaviour of such shells have been attempted. © 2005 Elsevier Ltd. All rights reserved.

Journal	Journal of Sound and Vibration
Publisher	Academic Press
ISSN	0022460X
Open Access	No