Optimal Design of Hysteretic Nonlinear Energy Sink for Suppression of Limit Cycle Oscillations of a Flapping Airfoil

Abstract

The aim of this study is to address the suppression of limit cycle oscillations (LCOs) of a flapping airfoil using hysteretic nonlinear energy sink (HNES). A flexible flapping wing with span-wise bending and twisting degrees of freedom incorporated through translation and torsional springs with nonlinear stiffness in heave and pitch is considered in this study. HNES is comprised of a mass connected with primary structure by a purely hysteretic and a linear elastic spring connected in parallel. The nonlinear hysteresis behaviour is characterized by Bouc–Wen model. The performance of HNES with negative stiffness is investigated. Numerical results presented in this paper clearly elucidated the enhanced performance of the proposed HNES with negative stiffness compared with conventional NES and HNES with positive stiffness. An optimization is carried out to find the optimal design parameters of HNES in a deterministic approach by considering uncertainties in initial conditions with the objective of minimizing peak and root mean square response of LCOs. The theoretical study in this paper clearly demonstrated the concept and efficiency of the proposed passive control strategy which can be easily adopted for existing and up-coming wings.