In this paper, the basic constitutive equations and equations of motion are derived to describe the behavior of thermoelastic porous piezoelectric medium by using Biot's theory and the theory of generalized thermoelasticity with on relaxation time (Lord-Shulman). The electrical enthalpy density function is derived in the general coordinates. Also, clear definitions for the poroelastic modulus, electrical, thermal and additional mixed coefficients are embedded. The uniqueness of the solution for the complete system of equations is presented.

this article presents the coupled thermoelasticity of a truncated functionally graded conical shell under thermal shock load. The classical coupled thermoelasticity theory is employed to set the partial differential equations of motion of the conical shell. The shell governing equations are based on the fi, rst-order shear deformation shell theory that accounts for the transverse shear strains and rotations. The solution is obtained by transforming the governing equations into the Laplace domain and using the Galerkin fi, nite element method in the Laplace domain to calculate the displacement components. The physical displacement components in real time domain are obtained by the numerical inversion of the Laplace transform. Temperature distribution is assumed to be linear across the shell thickness. Radial displacement, axial stress, axial force, and temperature versus time are calculated and the effect of relaxation time and power law index are examined. Comparison indicates that an increase in the radial vibration amplitude and a decrease of vibration frequency occur when changing the material from ceramic to metal. The results are validated with the known data in the literature.