MATEC Web Conf.
Volume 148, 2018International Conference on Engineering Vibration (ICoEV 2017)
|Number of page(s)||6|
|Section||Nonlinearity and Stochasticity in Vibrating Systems|
|Published online||02 February 2018|
Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
2 Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
The present paper investigates the effects of noisy flow fluctuations on the fluid-structure interaction (FSI) behaviour of a span-wise flexible wing modelled as a two degree-of-freedom elastically mounted flapping airfoil. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity exceeds a critical limit resulting in a stable limit-cycle oscillation (LCO) from a fixed point response. On the other hand, the qualitative dynamics changes from a stochastic fixed point to a random LCO through an intermittent state in the presence of irregular flow fluctuations. The probability density function depicts the most probable system state in the phase space. A phenomenological bifurcation (P-bifurcation) analysis based on the transition in the topology associated with the structure of the joint probability density function (pdf) of the response variables has been carried out. The joint pdf corresponding to the stochastic fixed point possesses a Dirac delta function like structure with a sharp single peak around zero. As the mean flow speed crosses the critical value, the joint pdf bifurcates to a crater-like structure indicating the occurrence of a P-bifurcation. The intermittent state is characterized by the co-existence of the unimodal as well as the crater like structure.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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