The study of nonlinear aeroelastic instability mechanism of nonconservative acousto-elastic system is the focus here. The acousto-elastic system consists of a spinning disc in a compressible fluid filled enclosure. The nonlinear rotating plate is coupled with the linear acoustic oscillations of the surrounding fluid. Based on the acousto-elastic theory, the coupled field equations are discretized and solved for various rotation speeds in order to obtain the coupled system dynamics. The study shows that the coupled system undergoes a flutter instability at a particular rotation speed and the instability takes the form of supercritical Hopf bifurcation. Subsequently, the effect of randomness associated with the structural and the acoustic damping parameters are quantified on the nonlinear instability behaviour by means of a spectral projection based polynomial chaos expansion technique. Copyright © 2016 by ASME.

Sunetra Sarkar

Department of Aerospace Engineering

W. Dheelibun Remigius

Bifurcation (mathematics)

ELASTICITY

Hopf bifurcation

Shafts (machine components)

stability

Wave propagation

ACOUSTIC OSCILLATION

AEROELASTIC INSTABILITIES

COUPLED FIELD EQUATIONS

Nonlinear instability

Polynomial chaos expansion

SPECTRAL PROJECTIONS

Supercritical Hopf bifurcation

Uncertainty quantifications

Aeroelasticity

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IIT Madras

ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

The paper focuses on application of uncertainty quantification techniques to a fluid structure interaction (FSI) problem involving a nonlinear rotating disc with surrounding fluid at high pressure without any dissipations. The deterministic dynamics shows strong influence of system parameters on the coupled FSI behavior. The nonlinear FSI problem has been discussed in detail and the instability mechanism has been presented. Such instabilities are known as flutter in closed medium and has significance in the turbomachinery industries. This gives way to a sudden large amplitude oscillation, known as the Hamiltonian Hopf bifurcation in such FSI systems. Uncertain variations in system parameters have been considered in order to see the effect on the flutter instability. Investigation with spectral uncertainty quantification tool has given the propagation of the input uncertainties on the instability behavior. © 2016 The Authors.

Fulltext

Procedia Engineering

Uncertainty Quantification of a Non-linear Rotating Plate Behavior in Compressible Fluid Medium

The present study focuses on the uncertainty quantification of an aeroelastic instability system. This is a classical dynamical system often used to model the flow induced oscillation of flexible structures such as turbine blades. It is relevant as a preliminary fluid-structure interaction model, successfully demonstrating the oscillation modes in blade rotor structures in attached flow conditions. The potential flow model used here is also significant because the modern turbine rotors are, in general, regulated in stall and pitch in order to avoid dynamic stall induced vibrations. Geometric nonlinearities are added to this model in order to consider the possibilities of large twisting of the blades. The resulting system shows Hopf and period-doubling bifurcations. Parametric uncertainties have been taken into account in order to consider modeling and measurement inaccuracies. A quadrature based spectral uncertainty tool called polynomial chaos expansion is used to quantify the propagation of uncertainty through the dynamical system of concern. The method is able to capture the bifurcations in the stochastic system with multiple uncertainties quite successfully. However, the periodic response realizations are prone to time degeneracy due to an increasing phase shifting between the realizations. In order to tackle the issue of degeneracy, a corrective algorithm using constant phase interpolation, which was developed earlier by one of the authors, is applied to the present aeroelastic problem. An interpolation of the oscillatory response is done at constant phases instead of constant time and that results in time independent accuracy levels. Copyright © 2013 by ASME.

Journal of Vibration and Acoustics, Transactions of the ASME

Uncertainty quantification of a nonlinear aeroelastic system using polynomial chaos expansion with constant phase interpolation

Aeroelastic stability remains an important concern for the design of modern structures such as wind turbine rotors, more so with the use of increasingly flexible blades. A nonlinear aeroelastic system has been considered in the present study with parametric uncertainties. Uncertainties can occur due to any inherent randomness in the system or modeling limitations, and so forth. Uncertainties can play a significant role in the aeroelastic stability predictions in a nonlinear system. The analysis has been put in a stochastic framework, and the propagation of system uncertainties has been quantified in the aeroelastic response. A spectral uncertainty quantification tool called Polynomial Chaos Expansion has been used. A projection-based nonintrusive Polynomial Chaos approach is shown to be much faster than its classical Galerkin method based counterpart. Traditional Monte Carlo Simulation is used as a reference solution. Effect of system randomness on the bifurcation behavior and the flutter boundary has been presented. Stochastic bifurcation results and bifurcation of probability density functions are also discussed. Copyright © 2010 Ajit Desai and Sunetra Sarkar.

Mathematical Problems in Engineering

Analysis of a nonlinear aeroelastic system with parametric uncertainties using polynomial chaos expansion

Volume 5: Design, Analysis, Control and Diagnosis of Fluid Power Systems

Natural Frequencies of Centrifugal Compressor Impellers for High Density Gas Applications

Journal of Sound and Vibration

Spectral and multiresolution Wiener expansions of oscillatory stochastic processes

Bifurcations and uncertainty quantifications in nonlinear acousto-elastic systems

Journal	ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)
Publisher	American Society of Mechanical Engineers (ASME)
Open Access	No