Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects

Based on the theory of surface piezoelectricity and nonlocal piezoelectricity, a novel two-dimensional theory of piezoelectric nanoplates and boundary conditions are derived by utilizing the Hamilton's principle. The free and forced vibrations of piezoelectric ceramic circular nanoplates are first investigated with the derived two-dimensional equations. Closed-form solutions are obtained and surface effects are examined. The results presented in this paper can be reduced to some classical ones theoretically and numerically. It has been revealed that the surface and nonlocal effects have a great influence on the performance of piezoelectric circular nanoplates in terms of resonant frequency, displacement, stress, electrical potential, current, capacitance ratio, and other quantities. A critical thickness of piezoelectric plate is calculated for the first time, below which the size-dependent effect is obvious that must be considered. These findings can provide effective guidance for the explanation of certain physical phenomenon about size-dependent electromechanical characteristics and experimental design of piezoelectric devices in nanoscale.