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

摘要

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. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim