Vibration characteristics of piezoelectric functionally graded carbon nanotube-reinforced composite doubly-curved shells

Abstract This paper presents an analytical solution for the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shells with integrated piezoelectric layers. Here, linear distribution electric potential across thickness layer and five different types nanotube (CNT) distributions through direction are considered. Based on four-variable shear deformation refined shell theory, governing equations obtained by applying Hamilton’s principle. Navier’s panels simply supported boundary condition at all four edges is derived. Several numerical examples validate accuracy presented solution. New parametric studies regarding effects material properties, geometric parameters, electrical conditions responses hybrid investigated discussed in detail.