Two-frequency parametric excitation and combination resonance of a nanocomposite laminated piezoelectric trapezoidal plate in subsonic airflow

Abstract

In this study, an analytical approach is presented to analyze the bifurcations and nonlinear dynamics of a cantilevered piezoelectric nanocomposite trapezoidal actuator subjected to two-frequency parametric excitations in the presence of subsonic airflow. The assumption of uniformly distributed single-walled carbon nanotubes along the thickness is taken into the consideration. The governing equations are built by the von-Karman nonlinear strain-displacement relations to consider the geometrical nonlinearity and the linear potential flow theory. The present study focuses on a specific resonance case deals with the occurrence of simultaneous resonances in the principal parametric resonance of the first mode and combination of the parametric resonance of the difference type involving two modes. The multiple scales method is employed to obtain the four nonlinear averaged equations which are solved by using the Runge-Kutta method. Moreover, the frequency-response curves, bifurcation diagrams, time history responses, and phase portrait are obtained to find the nonlinear dynamic responses of the plate. The effects of the amplitude of piezoelectric excitation, piezoelectric detuning parameter, and aerodynamic pressure are also studied. The results indicate that, the chaotic, quasi-periodic and periodic motions of the plate exist under certain conditions and the variation of controlling parameters can change the form of motions of the nanocomposite piezoelectric trapezoidal thin plate.