Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates

• More accurate dispersion analysis for piezoelectric nanoplates is performed.
• A nanoscale plate model including surface piezoelectricity and nonlocal small-scale is developed.
• Size-dependent behaviors of the dispersive modes are predicted.
• In the presence of nonlocal effect, elastic waves may vanish above a certain frequency.

In this paper, the dispersion characteristics of elastic waves propagating in a monolayer piezoelectric nanoplate is investigated with consideration of the surface piezoelectricity as well as the nonlocal small-scale effect. Nonlocal electroelasticity theory is used to derive the general governing equations by introducing an intrinsic length, and the surface effects exerting on the boundary conditions of the piezoelectric nanoplate are taken into account through incorporation of the surface piezoelectricity model and the generalized Young–Laplace equations. The dispersion relations of elastic waves based on the current formulation are obtained in an explicit closed form. Numerical results show that both the nonlocal scale parameter and surface piezoelectricity have significant influence on the size-dependent properties of dispersion behaviors. It is also found that there exists an escape frequency above which the waves may not propagate in the piezoelectric plate with nanoscale thickness.