This work presents the modelling of acoustic wave-based devices of various geometries through a mapped orthogonal functions method. A specificity of the method, namely the automatic incorporation of boundary conditions into equations of motion through position-dependent physical constants, is presented in detail. Formulations are given for two classes of problems: (i) problems with guided mode propagation and (ii) problems with stationary waves. The method’s interest is demonstrated by several examples, a seven-layered plate, a 2D rectangular resonator and a 3D cylindrical resonator, showing how it is easy to obtain either dispersion curves and field profiles for devices with guided mode propagation or electrical response for devices with stationary waves. Extensions and possible further developments are also given.

Study of guided waves in inhomogeneous elastic bodies has been an important area of solid mechanics for well over a century. Initial studies in the plates were applied to analyze surface acoustic waves in semi-infinite substrates and multilayered structures. Recently, several investigations have been reported on the axial propagation of guided waves in Functionally Graded Materials (FGMs). An FGM is essentially an inhomogeneous material composite, made up of two or more materials chosen to obtain desirable properties for specific applications. In this study, properties of the material such as Young's modulus, Poisson's ratio and mass density, are assumed to vary in the direction of the thickness according to a known radial variation law. Normalized frequencies of the guided acoustic modes are calculated as a function of normalized thickness. Dispersion curves and field profiles are presented for certain specific modes. The developed software is capable of dealing efficiently and accurately with a variety of homogeneous and inhomogeneous cylinders.