Nonlinear Electro-aero-elastic Vibration Analysis of a Nanocomposite Laminated Trapezoidal Actuator

The nonlinear dynamic and vibration behaviors of a cantilever carbon nanotube reinforced composite trapezoidal plate with two surface-bonded piezoelectric layers as an actuator in micro air vehicles which exposed to subsonic airflow under combined parametric and external excitations are considered in this paper. The plate is reinforced by single-walled carbon nanotubes. The large deflection Von Karman plate assumptions and the classical laminated plate theory are applied to derive the governing equations of the motion of the piezoelectric nanocomposite laminated trapezoidal plate by using the Hamilton’s principle. The geometry of trapezoidal plate is mapped into rectangular computational domain. The Galerkin’s approach is used to transform the nonlinear partial differential equations of motion into nonlinear two-degrees-of-freedom ordinary differential equations of cubic nonlinearities. The case of 1:3 internal resonance and primary resonance is considered and the multiple scales method is employed. The aerodynamic pressure distribution formula is modeled by linear potential flow theory. The frequency-response curves, time history responses and phase portrait in free, forced and actuated vibrations cases are obtained to analyze the nonlinear dynamic behavior of the plate. The effects of different parameters such as the plate geometry, volume fraction of carbon nanotubes and different excitations on the nonlinear vibration of the laminated thin plate are also discussed. A complex softening nonlinearity with two peak in the higher mode is observed in frequency response curves.