Piezoelectricity and length scale effect on the vibrational behaviors of circular sandwich micro-plates

Abstract

In this paper, the vibrational behaviors of circular and annular sandwich micro-plates coupled with two piezoelectric layers are analytically studied. For defining the equations of motion, the Hamilton’s principle and the classical plate theory are used. In the micro-scale size, the properties of the material depend on dimensions, and therefore the modified couple stress theory is utilized to consider this effect. The electric potential of piezoelectric layers is obtained by satisfaction of the Maxwell equation. The natural frequencies for various boundary conditions in two kinds of open and close circuit electric conditions are calculated, and the effects of length scale and electrical field are studied. The results show that the natural frequencies for open piezoelectric micro-plates are larger than the closed ones.