Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varies in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and temperature field on the wave propagation and transient response of functionally graded plates are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and provide a theoretical basis for engineering applications.