Numerical investigation into discontinuity-induced bifurcations in an aeroelastic system with coupled non-smooth nonlinearities

Abstract

The present study focuses on investigating the bifurcation characteristics of a pitch-plunge aeroelastic system possessing coupled non-smooth nonlinearities, both in structural and aerodynamic fronts. To this end, a freeplay nonlinearity is considered in the stiffness of the pitch degree-of-freedom (DoF). The effects of dynamic stall arising due to large instantaneous angles-of-attack (AoA) are incorporated using the semi-empirical Leishman Beddoes (LB) aerodynamic model. A systematic response analysis is carried out to discern the bifurcation characteristics of the aeroelastic system considering the airspeed as the system parameter. At low airspeeds, a series of dynamical transitions, including aperiodic responses, occur predominantly due to the structural freeplay nonlinearity while the flow remains attached to the surface of the wing. However, beyond a critical value of airspeed, the system response is dominated by high amplitude pitch-dominated limit-cycle oscillations, which can be attributed to stall flutter. It is demonstrated that the freeplay gap plays a key role in combining the effects of structural and aerodynamic nonlinearities. At higher values of the freeplay gap, interesting discontinuity-induced bifurcation scenarios, such as grazing and boundary equilibrium bifurcations arise due to coupled nonlinear interactions, which can significantly impact the safety of the aeroelastic system.

Open Set Domain Adaptation for Classification of Dynamical States in Nonlinear Fluid Dynamical Systems

“…In this case, both structure and aerodynamic loads are modelled as nonlinear. The structure possesses a pitch freeplay nonlinearity, same as II-B2, and the aerodynamics is governed by dynamic stall nonlinearity [3], [26]. The equation of motion is given by Eqs.…”

“…Structural freeplay nonlinearity, which arises from loose hinges or worn parts, leads to a period-doubling route to chaos and subsequent divergent oscillations [23]. Aerodynamic nonlinearity induced by dynamic stall can lead to both subcritical [3], [4], [24] and supercritical Hopf bifurcation routes [25], as well as a period-doubling route to chaos [23], [26].…”

“…Consequently, the structural safety of these fluid dynamical systems is compromised by the sudden onset of these dynamical signatures. In response, both the aeroelastic and thermoacoustic communities have invested considerable efforts in predicting, preventing, and suppressing instabilities in their respective fluid dynamical systems [5], [12]- [14], [18]- [20], [26], [30]. However, in the case of pulse combustors, a type of thermoacoustic system, the intention is to operate with oscillatory combustion [10], [11], [21], [22], [31].…”

Advanced Numerical Algorithm for Non-smoothness Differential Equations: Integrating Fractional Interpolation with Predictive- Corrective Techniques

“…In the realms of science and engineering, a myriad of systems are defined by nonsmooth differential equations (NSDEs), which are regularly experienced in practical applications. Examples include aeroelastic systems [1,2], dry friction systems [3],…”

Experimental investigation on the synchronization characteristics of a pitch-plunge aeroelastic system exhibiting stall flutter

“…Thus, the bifurcation analysis of aeroelastic systems with a proper understanding of the underlying physical mechanisms is of seminal importance in engineering parlance. Of these nonlinear aeroelastic instabilities, perhaps one of the most crucial is the stall flutter 1,2 , which may cause the aeroelastic systems to oscillate with high-amplitude LCOs. Stall flutter arises due to aerodynamic nonlinearity in terms of dynamic stall.…”