Novel phenomena on snap-through and nonlinear vibrations of bistable ACPCL cantilever shell under combined external and parametric excitations for wind turbine blade, theory and experiment

To optimize the aerodynamic performance of the wind turbine blades, the bistable skin structures are used to regulate the blade shape of the wind turbines. The bistable elements are connected to the wind turbine blade skin, allowing the shape transformation without the need for continuous energy input. In this paper, the bistable elements are simplified as the bistable asymmetric cross-ply composite laminated (ACPCL) cantilever shell model to study the novel phenomena on the snap-through and nonlinear vibrations for the first time. The snap-through, resonant responses, fractal basin boundaries, threshold surfaces, global bifurcations and double-parameter multi-pulse chaotic dynamics are investigated for the bistable ACPCL cantilever shell under combined the external and parametric excitations. Considering the low-frequency primary, high-frequency primary and 1/2 subharmonic parametric resonances, the multiple scale perturbation (MSP) method is utilized to obtain the averaged equations for the bistable ACPCL cantilever shell. The amplitude-frequency curve and force-amplitude response curve are depicted for the bistable ACPCL cantilever shell. The extended Melnikov method is employed to explore the global bifurcations, threshold surfaces, fractal basin boundaries, and double-parameter multi-pulse chaotic motions for the bistable ACPCL cantilever shell. Through the theoretical analysis and numerical simulation, we observe that the parametric excitation has a substantial impact on the nonlinear vibrations of the bistable ACPCL cantilever shell. It is found that the parametric excitation results in the appearance of the critical instability-state chaotic vibrations, disrupts the regular shape of the attractor basins and reveals a more pronounced fractal structure. The complex double-parameter multi-pulse chaotic dynamics are examined for the bistable ACPCL cantilever shell subject to combined the external and parametric excitations. From the bifurcation diagrams, the vibration forms of the bistable ACPCL cantilever shell are distinguished. In the experiment, the nonlinear vibration characteristics for the bistable ACPCL cantilever shell are verified.