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The current manuscript is presented to study two-dimensional deformations in a nonhomogeneous, isotropic, rotating, magneto-thermoelastic medium in the context of Green-Naghdi model III. It is assumed that the functionally graded material has nonhomogeneous mechanical and thermal properties in the x-direction. The exact expressions for the displacement components, temperature field, and stresses are obtained in the physical domain by using normal mode technique. These are also computed numerically for a copper-like material and presented graphically to observe the variations of the considered physical variables. Comparisons of the physical quantities are shown in figures to depict the effects of angular velocity, nonhomogeneity parameter, and magnetic field.

Purpose The purpose of this study is to analyze the two-dimensional disturbances in a nonlocal, functionally graded, isotropic thermoelastic medium under the purview of the Green–Lindsay model of generalized thermoelasticity. The formulation is subjected to a mechanical load. All the thermomechanical properties of the solid are assumed to vary exponentially with the position. Design/methodology/approach Normal mode technique is proposed to obtain the exact expressions for the displacement components, stresses and temperature field. Findings Numerical computations have been carried out with the help of MATLAB software and the results are illustrated graphically. These are also calculated numerically for a magnesium crystal-like material and illustrated through graphs. Theoretical and numerical results demonstrate that the nonlocality and nonhomogeneity parameters have significant effects on the considered physical fields. Originality/value Influences of nonlocality and nonhomogeneity on the physical quantities are carefully analyzed for isothermal and insulated boundaries. The present work is useful and valuable for analysis of problems involving mechanical shock, nonlocal parameter, functionally graded materials and elastic deformation.

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