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Articles written by King, P.I.

  1. Millman, D.R., King, P.I., and Beran, P.S.. "Airfoil pitch-and-plunge bifurcation behavior with Fourier chaos expansions" Journal of Aircraft. 42 (2). MAR-APR 2005. pp. 376--384.

    A stochastic projection method is employed to obtain the probability distribution of pitch angle of an airfoil in pitch and plunge subject to probabilistic uncertainty in both the initial pitch angle and the cubic spring coefficient of the restoring pitch force. Historically, the selected basis for the stochastic projection method has been orthogonal polynomials, referred to as the polynomial chaos. Such polynomials, however, result in unacceptable computational expense for applications involving oscillatory motion, and a new basis, the Fourier chaos, is introduced for computing limit-cycle oscillations. Unlike the polynomial chaos expansions, which cannot predict limit-cycle oscillations, the Fourier chaos expansions predict both subcritical and supercritical responses even with low-order expansions and high-order nonlinearities. Bifurcation diagrams generated with this new approximate method compare well to Monte Carlo simulations.


  2. Millman, D.R., King, P.I., Maple, R.C., Beran, P.S., and Chilton, L.K.. "Estimating the probability of failure of a nonlinear aeroelastic system" Journal of Aircraft. 43 (2). MAR-APR 2006. pp. 504--516.

    A limit-cycle oscillation (LCO) can be characterized by a subcritical or supercritical bifurcation, and bifurcations are shown to be discontinuities in the stochastic domain. The traditional polynomial-chaos-expansion method, which is a stochastic projection method, is too inefficient for estimating the LCO response surface because of the discontinuities associated with bifurcations. The objective of this research is to extend the stochastic projection method to include the construction of B-spline surfaces in the stochastic domain. The multivariate B-spline problem is solved to estimate the LCO response surface. A Monte Carlo simulation (MCS) is performed on this response surface to estimate the probability density function (PDF) of the LCO response. The stochastic projection method via B-splines is applied to the problem of estimating the PDF of a subcritical LCO response of a nonlinear airfoil in inviscid transonic flow. A probability of failure based upon certain failure criteria can then be computed from the estimated PDF. The stochastic algorithm provides a conservative estimate of the probability of failure of this aeroelastic system two orders of magnitude more efficiently than performing an MCS on the governing equations.