Vibration analysis of size-dependent bimorph functionally graded piezoelectric cylindrical shell based on nonlocal strain gradient theory

Functionally graded piezoelectric materials (FGPMs) have emerged as promising candidates for electronic nanodevices. In this paper, a study on dynamic response of a bimorph FGP cylindrical nanoshell based on nonlocal strain gradient theory is presented. The material properties are assumed to be variable across thickness direction according to power law distribution. The electric potential is considered to be quadratic through thickness direction. The governing equations and boundary conditions are obtained on the basis of first-order shear deformation theory using Hamilton's principle. As case study, free vibration of simply supported bimorph FGP cylindrical nanoshell is studied and the influences of different parameters on natural frequency are illustrated. The results obtained provide detailed insights into dynamic response of bimorph FGP cylindrical nanoshell and provide evidence for its size dependency especially by increase in thickness and decrease in length, which is an important conclusion for obtaining appropriate functionality in sensors and actuators.