This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic, unbounded, rotating medium due to a periodically varying heat source in the context of the linear theory of generalized thermoelasticity without energy dissipation and with energy dissipation. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material under the influence of a magnetic field are established. The Laplace–Fourier double transform technique has been used to get the solution. The inversion of Fourier transform is done by using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerre’s method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. The numerical estimates for displacements, temperature and stress are obtained for a hypothetical material. The solution to the analogous problem is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of rotation, non-homogeneity, damping coefficient and magnetic field on displacements, temperature and stress. © 2015, Springer-Verlag Wien.