Nonlinear Vibrations of Piezoelectric Carbon Nanotube-Reinforced Composite Trapezoidal Actuator Under Strong Electric Field

In recent years, piezoelectric actuators have been extensively utilized in novel technologies such as insect-sized micro air vehicles. Utilization of common piezoceramics and high performance nanocomposite materials coupled with special geometry like trapezoidal plates which are driven at high electric field yields suitable actuators for use in such applications. First, in this paper the nonlinear vibrations of the carbon nanotube reinforced composites cantilever trapezoidal plate with two surface-bonded piezoelectric layers is modeled in accordance to classical laminate plate theory and large deflection Von Karman type equations for the geometric nonlinearity by using the Hamilton’s principle. The geometry of trapezoidal plate is mapped into rectangular computational domain. Second, the Galerkin discretization method is used for changing the partial differential equations into ordinary differential equations. Finally, the governing equations of the motion of piezoelectric laminated carbon nano-tube reinforced composite trapezoidal actuator with cubic nonlinearities under the external excitation and strong electric field with considering electroelastic and electrostrictive effects, is modeled and the linear natural frequency of transversal deflection is obtained.