Mathematical model and stability analysis of fluttering and autorotation of an articulated plate into a flow

This paper is dedicated to develop a mathematical model that can simulate nonlinear phenomena of a hinged plate which places into the fluid flow (1 DOF). These phenomena are fluttering (oscillation motion), autorotation (continuous rotation) and chaotic motion (combination of fluttering and autorotation). Two mathematical models are developed for 1 DOF problem using two eminent mathematical models which had been proposed for falling plates (3 DOF). The procedures of developing these models are elaborated and then these results are compared to experimental data. The best model in the simulation of the phenomena is chosen for stability and bifurcation analysis. Based on these analyses, this model shows a transcritical bifurcation and as a result, the stability diagram and threshold are presented. Moreover, an analytical expression is given for finding the boundary of bifurcation from the fluttering to the autorotation.