Nonlinear Dynamic Analysis and Control of FG Cylindrical Shell Fitted with Piezoelectric Layers

In this study, the nonlinear vibration control of functionally graded laminated piezoelectric cylindrical shells under simultaneous parametric axial and radial external excitations is presented. The partial differential equations of shells are derived based on Hamilton's principle, first-order shear deformation theory (FSDT), and nonlinear von Karman relations. The coupled nonlinear ordinary differential equations are obtained by Galerkin's procedure and solved by the method of static condensation. Two piezoelectric layers are placed on the outer and inner surfaces of the cylindrical shell each as distributed sensor and actuator. Then the constant-gain negative velocity feedback strategy is employed. Regarding the nonlinear equations of motion, for the first time, the vibration analysis and active vibration control of smart FG cylindrical shells under combined parametric and external excitations are analyzed using the multiple scales approach. The effects of various parameters such as power index, external excitation's amplitude, and control gain on the dynamic behavior of the system are investigated, using bifurcation diagrams, phase portraits, time histories, and Poincare maps. It is shown that quasi-periodic motion is the most common behavior of the system and controller gain and power index have inevitable effects on enhancing the quasi-periodic response of the system. Care should be exerted in selecting the parameters to have the desired response in the broad range of excitation frequency.