Complex nonlinear dynamical behaviors of the mechanical vibration system for the cantilever wing plate with variable cross-section: Experiment and theory

For the nonlinear dynamic characteristics of aircraft structures, the idealized models are often used to simplify the actual structure to reduce the complexity of the analysis and highlight the key response characteristics. The wing is usually modeled as a variable-section wing plate with cantilever boundary conditions, which effectively studied primary structural behaviors in nonlinear vibration. Considering the graphene-reinforced materials, we investigate the complex nonlinear dynamic behaviors of the cantilever wing plate with variable cross-section by using the experiments and theory. The nonlinear vibrational behaviors include the threshold surface, resonance responses, global bifurcations and double-parameter multi-pulse chaotic motions for the system subjected to the parametric and transverse excitations. The vibrational test experiments for the cantilever variable cross section plate are conducted before the theoretical investigation, which the results certify the existence of the complex dynamical behaviors for the mechanical vibration system. For the vibrational theory study of the variable-section wing plate with cantilever boundary conditions, considering the primary resonances, 1/2 sub-harmonic parametric resonances, and the 1:1 internal resonance, the averaged equations for the cantilever variable cross section wing plate are obtained through the multiple scale perturbation (MSP) method. The amplitude-frequency and force-amplitude response curves are depicted to examine the resonant responses. The extended Melnikov method is utilized to evaluate the threshold surface, global bifurcations and double-parameter multi-pulse chaotic dynamics for the system subjected to the parametric and transverse excitations. In the case of the simultaneous resonances, the system exhibits the classical nonlinear hard spring characteristics and two resonance peaks. Under larger parametric or transverse excitations, the nonlinear behavior of the first-order modes for the system becomes more pronounced, resulting in larger resonance peaks. In addition, multi-pulse homoclinic orbits emerge in the system, leading to double-parameter multi-pulse chaotic vibration characteristics under combined the parametric and transverse excitations. Alternating periodic and double-parameter multi-pulse chaotic motions appear for the system in the influence of the parametric and transverse excitations.