Analysis Of The Propagation Of Surface Acoustic Waves In Functionally Graded Material Plate

The propagation of elastic waves in functionally graded plates has wide applications in engineering. The analytical methods for the consideration of finite solids with structural complications have been subjecting to extensive research efforts. To obtain the velocity and deformation accurately, layered model, Forbenius method, and homotopy analysis method are employed to study the propagation of surface acoustic waves in functionally graded plates. Comparisons with results from different methods are made for validation and ranking. Cases with polynomial and exponential material property variation schemes are calculated with these methods, which show that the influences to the velocity and displacement model are different. In applications, the grading scheme must be chosen according to the displacement model. Also, we found that the layered model is simple in concept and implementation, but its convergence is slow. Although we can get the analytical solutions from Frobenius method, the derivation is complicate and its requirement for precise numerical evaluation is difficult to meet. Homotopy analysis method, on the other hand, can obtain the general solutions which include the Frobenius solution, and the rate of convergence can be improved by properly selecting parameters. We study the surface acoustic waves in functionally graded plate with the solution methods and property variation schemes, and obtained the velocity and deformation. This study provides a theoretical foundation for applications in engineering.In the first chapter, we briefly reviewed the concept and development of functionally graded material, and introduced the methods for the analysis of functionally graded structures. For the surface acoustic waves in functionally graded plates, we provide the layered model, Frobenius method, and the homotopy analysis method.In the second and third chapters, we analyzed the propagation of surface acoustic waves (Rayleigh waves) in functionally graded plates with the layered model and Frobenius method, respectively. Solutions from plates with exponential property grading schemes are obtained from the layered model and Frobenius method and comparisons with known analytical results are made to validate and evaluate the methods. We also analyzed cases with polynomial material property variation schemes.In the fourth chapter, we employed the homotopy analysis method (HAM) to analyze the propagation of surface acoustic wave in functionally graded plate. First, power series are used as the primary basis function, and obtained the same results as from the layered model and Frobenius method. To improve the rate and radius of convergence of power series, we made use of the analytical solutions of homogeneous plates and analyzed the problem again with the combination of power function and exponential function as primary basis function.In the fifth chapter, through comparison of the three methods, we found that the solution of Frobenius method is included in that of the HAM.In the sixth chapter, by analyzing the propagation of surface acoustic waves in functionally graded plates, we obtained some conclusions significant for resonator and other engineering applications.