Nonlinear vibration of a nanocomposite laminated piezoelectric trapezoidal actuator in subsonic airflow under combined electrical and forcing excitations

Abstract

The nonlinear dynamic and vibration behaviors of a cantilevered carbon nanotube-reinforced composite trapezoidal plate with two surface-bonded piezoelectric layers as an actuator in micro air vehicles are considered in this article. The plate is reinforced by single-walled carbon nanotubes and is exposed to subsonic airflow under combined parametric and external excitations. 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 Hamilton's principle. The geometry of the trapezoidal plate is mapped into a rectangular computational domain. The Galerkin's approach is used for transforming 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 and time history responses and phase portrait in free forced vibrations 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 thin laminated plate are also discussed. A complex softening nonlinearity with two peaks in the higher mode is observed in frequency response curves. The influence of electrical excitation with several amplitudes and frequencies on dynamic stability is investigated using time response curves.

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

“…The two-degrees-of-freedom non-dimensional governing differential equations of the transverse motion of the laminated trapezoidal plate (in Figure 1(b)), with cubic nonlinearities due to large deflection and subjected to parametric and external excitations, and aerodynamic pressure were obtained by Noroozi and Bakhtiari-Nejad. 43 …”

“…The subsonic airflow with density ρ∞ and velocity U∞ is over the top side of the plate, so the trapezoidal plate is subjected to the aerodynamic pressure ΔP which can be modeled based on Bernoulli’s equations by the linear potential flow theory and it is expressed as 43,46 …”

“…Thus, it is difficult to give comparisons between our study and the works of other researchers. But, some simple case validation, for example, linear frequencies of the two modes and free vibration, of the plate model were done in ref [43].…”

“…42 They focused on the principal and 1:3 internal resonances of the plate. Also, Noroozi and Bakhtiari-Nejad 43 investigated the nonlinear vibration behaviors of a cantilevered CNTRC trapezoidal plate with two surface-bonded piezoelectric layers as an actuator in micro air vehicles. The plate was subjected to the subsonic airflow and combined parametric and external excitations.…”

“Nonlinear Dynamics of Mechanical Systems” dedicated to 75th birthday and 52 years scientific contribution of Prof. Katica R. (Stevanovic) Hedrih

“…The articles with multi-physics structural mechanics include electromechanical coupling [Mitura and Warminski, Zhang et al, Rocha et al] [18][19][20] electro-fluid-structural coupling [Karlicic et al, Noroozi and Bakhtiari-Nejad] 21,22 and thermomechanical coupling Iarriccio et al 23 Electromechanical coupling for control has been performed in [Mitura and Warminski, Zhang et al] 18,19 . Mitura and Warminski 18 in a beam with inertia and geometric nonlinearities electromechanically coupled nonlinearly with a controller, applied active vibration control with a nonlinear saturation algorithm whereas the impact of hysteresis of the piezoelectric system is considered.…”