Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory

Abstract In this study, the governing equations of electromechanical vibration of cylindrical nanoshell made of functionally graded piezoelectric material (FGPM) are developed using the consistent couple stress theory and the cylindrical shell model. The new consistent couple stress has only one material length scale parameter and is able to consider size effects relating to the nanoshell structure in the nanoscale. The governing equations and boundary conditions are determined using the energy method and Hamilton’s principle. Afterwards, using Navier and Galerkin methods, the free vibration of a special model of FGPM nanoshell under different boundary conditions are investigated. Finally, the effect of different parameters such as dimensionless length scale parameter, variation of index, length-to-radius ratio, and radius-to-thickness ratio are investigated. It is demonstrated that the length-to-radius ratio, radius-to-thickness ratio, and dimensionless length scale parameter play a significant role in the vibration behavior of the FGPM cylindrical nanoshell based on the size-dependent piezoelectric theory.