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STOCHASTIC BIFURCATION ANALYSIS OF AN ELASTICALLY MOUNTED FLAPPING AIRFOIL IN AN INVISCID FLUID
Last modified: 2017-07-03
Abstract
Biological flyers take the advantage of FSI to augment their propulsive efficiency by exploiting the coupling between the flexible wings and the surrounding unsteady flow-field. A proper understanding of the role of FSI in natural flights is essential
for the design of biologically-inspired Micro Aerial Vehicles (MAVs). In field conditions, the flow is typically accompanied by irregular fluctuations which significantly affect the performance of very light weight flapping wing MAVs, that are primarily aimed for indoor applications. The present study focusses on carrying out a stochastic bifurcation analysis to understand the effects of fluctuating flow on the dynamical stability characteristics of the coupled dynamical system. In this study, a span-wise
flexible wing has been modelled by an elastically mounted airfoil supported by a translational and a rotational cubic nonlinear springs along the plunge (bending) and pitch (torsion) degrees of freedom respectively. The nonlinear structural model has been
coupled with an inviscid flow solver using a weak coupling strategy to build the FSI framework. The flow part is solved using the unsteady vortex lattice method (UVLM). A bifurcation analysis has been carried out considering the mean wind speed to
be the bifurcation parameter. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity is increased resulting in a stable limit-cycle oscillation (LCO) from a fixed point response. However, the qualitative dynamics
changes from a stochastic fixed point to a random LCO through an on-off intermittent state as a long time scale gust has been imposed on the present system. A P-bifurcation analysis based on the transition in the topology associated with the structure of the joint pdf of the response variables reveals that the joint pdf corresponding to the stochastic fixed point response (Fig. 1(a)) possesses a direct delta function like structure with a sharp single peak around zero at a very low mean wind speed. As the mean wind speed increased, one can see in the joint pdf that along with the peak around zero value, a new weak attractor has been born highlighting the periodic bursts in the on-off intermittent phase (Fig. 1(b)). As the mean wind speed is further increased and it crosses the critical value, the joint pdf bifurcates to a crater-like structure corresponding to the random LCO which denotes the occurrence of a P-bifurcation (Fig. 1(c)). Moreover, the present paper further focusses on the stochastic bifurcations of the coupled system in the post-flutter regime in the presence of an actuating force which will be presented in the full paper.
for the design of biologically-inspired Micro Aerial Vehicles (MAVs). In field conditions, the flow is typically accompanied by irregular fluctuations which significantly affect the performance of very light weight flapping wing MAVs, that are primarily aimed for indoor applications. The present study focusses on carrying out a stochastic bifurcation analysis to understand the effects of fluctuating flow on the dynamical stability characteristics of the coupled dynamical system. In this study, a span-wise
flexible wing has been modelled by an elastically mounted airfoil supported by a translational and a rotational cubic nonlinear springs along the plunge (bending) and pitch (torsion) degrees of freedom respectively. The nonlinear structural model has been
coupled with an inviscid flow solver using a weak coupling strategy to build the FSI framework. The flow part is solved using the unsteady vortex lattice method (UVLM). A bifurcation analysis has been carried out considering the mean wind speed to
be the bifurcation parameter. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity is increased resulting in a stable limit-cycle oscillation (LCO) from a fixed point response. However, the qualitative dynamics
changes from a stochastic fixed point to a random LCO through an on-off intermittent state as a long time scale gust has been imposed on the present system. A P-bifurcation analysis based on the transition in the topology associated with the structure of the joint pdf of the response variables reveals that the joint pdf corresponding to the stochastic fixed point response (Fig. 1(a)) possesses a direct delta function like structure with a sharp single peak around zero at a very low mean wind speed. As the mean wind speed increased, one can see in the joint pdf that along with the peak around zero value, a new weak attractor has been born highlighting the periodic bursts in the on-off intermittent phase (Fig. 1(b)). As the mean wind speed is further increased and it crosses the critical value, the joint pdf bifurcates to a crater-like structure corresponding to the random LCO which denotes the occurrence of a P-bifurcation (Fig. 1(c)). Moreover, the present paper further focusses on the stochastic bifurcations of the coupled system in the post-flutter regime in the presence of an actuating force which will be presented in the full paper.