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Analysis of complicated one‐dimensional stress oscillation behaviour in a functionally graded material plate

A one‐dimensional elastodynamic problem in a functionally graded material (FGM) plate subjected to an impact pressure is analyzed in this paper. Applying techniques of the space‐variable transformation and Laplace transform, exact analytical solutions are derived for two cases of variations in material properties when nonhomogeneous material properties are expressed as exponential functions of the space‐variable. Numerical calculations for time histories of stresses have been carried out. Analytical and numerical results reveal that the stress oscillation obtained from one analytical solution is complicated and quasi‐periodic when the mechanical impedance depends on the space‐variable, whereas it derived from the other analytical solution is monotonic and periodic when the impedance is independent of the space‐variable. The factor which causes the different behaviours is also investigated based on the analytical and numerical results. This effect could be a key to controlling a complicated stress oscillation in an FGM plate.