Effect of the rotation of generalized thermoelastic layer subjected to harmonic heat: state-space approach

The theory of generalized thermoelasticity, based on the theory of Lord–Shulman (L-S) with one relaxation time, is used to solve boundary value problems of a one-dimensional layer of semi-infinite elastic medium. We considered the medium is rotating, and one of its boundaries subjected to harmonic heat and traction free, and the other boundary connected to the rigid foundation and has zero heat flux. The governing partial differential equations are solved in the Laplace transform domain by using the state-space approach of the modern control theory. The inverse Laplace transforms are obtained numerically. The temperature, the displacement, and the stress distributions are represented graphically with some comparisons to stand on the effect of the rotation of the medium and the harmonic heat on all the studied functions.