Acoustic wave propagation through a functionally graded material plate with arbitrary material properties

Abstract

In this article, the propagation of one-dimensional stress waves in a plate made of functionally graded materials excited by a harmonic force is studied. The material properties of the functionally graded material plate are assumed to be graded in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The governing equations are based on stress–strain relation and the equation of motion. Keeping generality, the functionally graded material plate is assumed as a multilayer with linear material property in each layer while arbitrary exponential material property through the thickness. A plate made of aluminum and alumina is considered as an example to illustrate the effects of the volume fraction exponent and number of layers on the wave propagation characteristics. Results indicate that by changing the exponent values ( M), stress distribution can be controlled. Also at every certain power law ( M), there exist a number of layers beyond which no variation in stress can be detected on the plate response. Furthermore, the wave in time domain is also investigated and the effects of material distribution on the wave speed are examined.