Exact Solution for Electrothermoelastic Behaviors of a Radially Polarized FGPM Rotating Disk

Document Type: Research Paper

Authors

1 Faculty of Mechanical Engineering, University of Kashan,

2 Faculty of Mechanical Engineering, University of Kashan

3 Department of Chemical Engineering, Faculty of Engineering, University of Kashan

Abstract

This article presents an exact solution for an axisymmetric functionally graded piezoelectric (FGP) rotating disk with constant thickness subjected to an electric field and thermal gradient. All mechanical, thermal and piezoelectric properties except for Poisson’s ratio are taken in the form of power functions in radial direction. After solving the heat transfer equation, first a symmetric distribution of temperature is produced. The gradient of displacement in axial direction is then obtained by assuming stress equation in axial direction to be zero. The electric potential gradient is attained by charge and electric displacement equations. Substituting these terms in the equations for the dimensionless stresses in the radial and circumferential directions yield these stresses and using them in the mechanical equilibrium equation a nonhomogeneous second order differential equation is produced that by solving it, the dimensionless displacement in radial direction can be achieved. The study results for a FGP rotating hollow disk are presented graphically in the form of distributions for displacement, stresses and electrical potential.

Keywords


[1] Galic D., Horgan C.O., 2002, Internally pressurized radially polarized piezoelectric cylinders, Journal of Elasticity 66: 257-272.

[2] Chen W.Q., Lu Y., Ye J.R, Cai J.B., 2002, 3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loading, Archive of Applied Mechanics 72: 39-51.

[3] Ding H.J., Wang H.M.,Chen W.Q., 2003, Dynamic responses of a functionally graded pyroelectric hollow sphere for spherically symmetric problems, International Journal of Mechanical Sciences 45: 1029-1051.

[4] Ding H.J., Wang H.M., Chen W.Q., 2004, Analytical solution of a special non-homogeneous pyroelectric cylinder for piezothermoelastic axisymmetric plane strain dynamic problems, Applied Mathematics and Computation 151: 423-441.

[5] Dai H.L., Wang X., 2005, Thermo-electro-elastic transient responses in piezoelectric hollow structures, International Journal of Solids and Structures 42: 1151-1171.

[6] Chen Y., Shi Z.F., 2005, Analysis of a functionally graded piezothermoelastic hollow cylinder, J Zhejiang Univ SCI 6A: 956-961.

[7] Hosseini Kordkheili S.A., Naghdabadi R., 2007, Thermoelastic analysis of a functionally graded rotating disk, Composite Structures 79: 508-516.

[8] Bayat M., Saleem M., Sahari B.B., Hamouda A.M.S., Mahdi E., 2007, Thermo elastic analysis of a functionally graded rotating disk with small and large deflections, Thin-Wall Structures 45: 677-691.

[9] Bayat M., Sahari B.B., Saleem M., Hmouda A.M.S., Reddy J.N., 2009, Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness, International Journal of Mechanics and Mastererial Design 5: 263:279.

[10] Bayat M., Sahari B.B., Saleem M., Hmouda A.M.S., Wong S.V., Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory, Thin-Wall Structures 47: 568-582.

[11] Ootao Y., Tanigawa Y. 2007, Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere, Composite Structures 81: 540-549.

[12] Saadatfar M., Razavi A.S., 2009, Piezoelectric hollow cylinder with thermal gradient, J Mech Sci Technol 23: 45-53.

[13] Asghari A., Ghafoori E., 2010, A three-dimensional elasticity solution for functionally graded rotating disks, Composite Structures 92: 1092-1099.

[14] Khoshgoftar M.J., Ghorbanpour Arani A., Arefi M., 2009, Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Materials and Structures 18: 115007.

[15] Hassani A., Hojjati M.H., Farrahi G., Alashti R.A., 2011, Semi-exact elastic solution for thermo-mechanical analysis of functionally graded rotating disks, Composite Structures 93: 3239-3251.

[16] Hassani A., Hojjati M.H., Farrahi G., Alashti R.A., 2012, Semi-exact solution for thermo-mechanical analysis of functionally graded elastic-strain hardening rotating disks, 17: 3747-3762.

[17] Jabbari M., Sobhanpour S., Eslami M.R., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessels and Piping 79: 493-497.

[18] Yang J., 2005, An introduction to the theory of piezoelectricity. Springer Science, Inc. Boston.