The state-vector formalism and the Peano-series solution for modelling guided waves in functionally graded anisotropic piezoelectric plates

Propagation of guided acoustic waves in infinite functionally graded piezoelectric plates is considered. In contrast to commonly used discretization of a continuous through-plate variation of material properties, our approach involves an exact solution to the problem in the form of the Peano series of multiple integrals, which is plugged into the state-vector formalism. With a view to enhance efficiency of the method, a special effort is made towards revealing a full scope of analytical properties and algebraic symmetries of the propagator and impedance matrices of the state-vector formalism for both homogeneous and functionally graded anisotropic piezoelectric plates. A clear distinction is established between the inhomogeneity–invariant properties, which are related to the energy considerations, and the properties, which are sensitive to the presence of inhomogeneity (these are notably different for symmetric and asymmetric profiles). Various formulations of the involved matrix tools are detailed and adapted into a unified framework fitting different electrical boundary conditions and an optional choice of the dispersion variables. The numerical implementation is exemplified for a homogeneous LiNbO3 plate, suitable for highlighting effects of strong piezoelectric coupling, and for a functionally graded plate. A good agreement is observed between the present computations and results obtained by other methods.