Development of an efficient, novel hybrid flutter-based wind energy harvester and identification of its delay characteristics and hysteretic behavior—Part Ⅱ: Theoretical modeling, analysis, and simulations

The second of two parts, this paper presents the theoretical modeling, analysis, and simulation of a novel, efficient hybrid flutter-based wind energy harvester. The theoretical examinations focus on structural dynamics, the modeling of the elastic restoring force, and the formulation of unsteady aerodynamic responses. A three-degree-of-freedom discrete structural model is developed to describe the plunging and pitching motions of the airfoil. The nonlinear magnetic spring is combined with a nonlinear aerodynamic model constructed using time-delay operators, which yields a set of coupled, autonomous nonlinear differential equations with multiple time delays. The model successfully captures the system’s instability and hysteresis phenomena, including jump behaviors. Through a series of extensive finite-element computations, we develop nonlinear expressions for the aerodynamic forces and moments in terms of wind velocity. The structural model is derived by combining the extended Hamilton’s principle with the aerodynamic model to obtain a complete system of delay differential equations (DDEs). After identifying the optimal configuration and validating its parameters, the DDEs, along with the associated phase (or time)-delay effects and eigenvalue problem, are solved to evaluate the system’s stability and predict its dynamic response—including the hysteretic behavior accompanying the jump phenomena—and energy-harvesting performance. The model’s predictions agree closely with the experimental results, which confirms the accuracy and reliability of the proposed modeling framework.