Characteristics of nonlinear vibration of nanocomposite cylindrical shells with piezoelectric actuators under thermo-mechanical loads

The paper presents an investigation of electro-thermo-mechanical vibration of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells surrounded by an elastic medium by an analytical approach. The uniform and functionally graded CNTs are used to reinforce through the thickness of the shell. Based on geometrical nonlinearity in von Karman-Donnell's sense within the classical thin shell theory, the governing equations of motion are proposed. By using the Galerkin's method to solve the equations of motion, analytical solutions with three approximate functions of deflection are given to analyze thermal vibration of the piezoelectric actuated FG-CNTRC shells. Piezoelectric layers are bonded onto the outer and inner surfaces of the cylindrical shell to act as the actuators, respectively. The Dormand/Prince Runge-Kutta pairs are used as a semi-analytical approach to solve differential equations of the problem. The fundamental frequencies, relation of frequency ratios-amplitudes and responses of vibration are researched. Furthermore, the effects of CNT volume fraction, piezoelectric layers, thermal environment, distribution type of the reinforcement, geometrical parameters and elastic foundation are analyzed. It is expected that the obtained results can be used as benchmark solutions for an analytical approach to serve in further research as well as in industrial applications.