Analysis of a Nonlinear Aeroelastic System with Parametric Uncertainties Using Polynomial Chaos Expansion

Ajit Desai · Sunetra Sarkar

35 citations0/0 files storedMathematical Problems in Engineering

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Probabilistic and Robust Engineering Design Vibration and Dynamic Analysis Aeroelasticity and Vibration Control

Abstract

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.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2005High-Order Collocation Methods for Differential Equations with Random Inputs 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 2009An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis 2002Error and uncertainty in modeling and simulation 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure

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