Guided wave characteristics in functionally graded piezoelectric rings with rectangular cross-sections

For the purpose of design and optimization of functionally graded piezoelectric material (FGPM) transducers, wave propagation in FGPM structures has received much attention in the past twenty years. But previous research efforts have been focused essentially on semi-infinite structures and one-dimensional structures, i.e., structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper proposes a double orthogonal polynomial series approach to solving the wave propagation problem in a two-dimensional FGPM structure, namely an FGPM ring with a rectangular cross-section. By numerical comparison with the available reference results for a purely elastic homogeneous rectangular rod, the validity of the extended polynomial approach is illustrated. The dispersion curves and the electric potential distributions of various FGPM rectangular rings with different material gradient directions, different polarization directions, different radius to thickness ratios, and different width to thickness ratios are calculated to reveal the guided wave characteristics