Deformation in transversely isotropic thermoelastic medium using new modified couple stress theory in frequency domain

Abstract

The objective of this paper is to study the two dimensional deformation in transversely isotropic thermoelastic medium without energy dissipation due to time harmonic sources using new modified couple stress theory, a continuum theory capable to predict the size effects at micro/nano scale. The couple stress constitutive relationships have been introduced for transversely isotropic thermoelastic medium, in which the curvature tensor is asymmetric and the couple stress moment tensor is symmetric. Fourier transform technique is applied to obtain the solutions of the governing equations. Assuming the deformation to be harmonically time-dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed sources have been considered to show the utility of the solution obtained. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of angular frequency are depicted graphically on the resulted quantities.