Analytical studies of surface acoustic waves in solids of functionally graded materials

Some traditional applications of structures and devices with homogeneous materials are being gradually replaced by functionally graded materials (FGM) with spatial variation of properties. The analysis of surface acoustic waves (SAW) propagating in FGM structures will be different primarily due to variations of material properties and resulted differential equations with variable coefficients. With the exception of a few patterns of variation, analytical solutions of wave propagation in FGM cannot be obtained. As a result, there will be challenges in the validation of numerical and approximate solutions. To meet the need for exact solutions, we studied the surface acoustic waves propagating in an FGM plate with the layered method, the Frobenius method, and the homotopy analysis method (HAM) for analytical and exact solutions. These three methods represent available techniques for analytical solutions of a large class of problems with important applications in the FGM structures. Numerical results based on the three methods are given for FGM plates with material property variations in a linear pattern. These analytical examples are presented along with detailed explanations of the methods and formulation to demonstrate the effectiveness of the methods and the effect of FGM on changes of plate deformation and frequency effects in SAW propagation with possible applications in devices and structures.