Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials (FGMs) have been done by researchers, but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates. This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM. This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function. The FGM plate is assumed to consist of a mixture of metal and ceramic, and its properties change depending on the power functions of the thickness of the plate, such as linear, quadratic, cubic, and inverse quadratic. By utilizing Hamilton’s principle, general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate, including the effects of changing compositional characteristics of materials.