Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory

A size-dependent functionally graded piezoelectric microplate model is developed in this paper. It is based on the modified couple-stress and sinusoidal plate theories. The main advantages of the modified couple-stress theory over the classical couple-stress theory are the introduction of the symmetric couple-stress tensor and the involvement of only one material length-scale parameter. The material properties of functionally graded piezoelectric plate are assumed to vary through the thickness according to a power law. Numerical examples are presented for both static bending and free vibration problems of a simply supported piezoelectric functionally graded microplate. The effects of power-law index of material gradient, material length-scale parameter, plate aspect ratio, and mechanical and electric loadings on the displacement (deflection), electric potential, stress, electric displacement and natural frequency are demonstrated.