Investigations of the Vibrational Design and Nonlinear Dynamic for the Three-Phase Graphene and Fiber-Reinforced Aluminum-based Laminated Composite Cantilever Trapezoidal Wing Plate

For the increasing demand of better dynamic performance and fuel efficiency in next-generation aircraft, the structural design for the wing plate needs to consider lightweight materials with superior mechanical properties. With high mechanical strength and low mass density, graphene-reinforced composites represent an excellent option for lightweight structural design. In this paper, comparative design analyses are conducted for a three-phase graphene and titanium fiber-reinforced (G-TFR) aluminum-based cantilevered trapezoidal laminated composite wing plate based on its natural vibration characteristics. Moreover, the nonlinear dynamic responses under dual-parameter excitations are systematically investigated to reveal the complex vibration behavior. The mechanical properties of the three-phase G-TFR aluminum-based composites are evaluated using the Halpin–Tsai model combined with the elastic theory. Under combined harmonic and parametric excitations, the nonlinear governing model with geometric large deformation is formulated for the three-phase G-TFR aluminum-based trapezoidal aerofoil panel based on the classical laminated plate theory in conjunction with Hamilton’s principle. The natural frequencies of the structure are obtained using the Rayleigh–Ritz method. The results are verified and validated against finite element analysis by applying Comsol Multiphysics. The primary resonance is investigated for the three-phase G-TFR aluminum-based laminated composite trapezoidal wing plate. The multi-pulse chaotic responses under dual-parameter excitations, which are transverse and parametric excitations, are depicted by using the Runge–Kutta method. For the different combinations of the volume content, spatial distribution of graphene and laying angle of the fiber, the influences of the first three natural frequencies are different. In addition, the system exhibits a hardening nonlinear behavior and the double-parameter dynamical behaviors are more complex when the system is subject to coupled parametric and transverse excitations.