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Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters. (English) Zbl 1236.74071

Summary: The limit cycle oscillation of a two-dimensional airfoil with parameter variability in an incompressible flow is investigated using the incremental harmonic balance (IHB) method. The variable parameters, such as the wind speed, the cubic plunge and pitch stiffness coefficients, are modeled as either bounded uncertain or stochastic parameters. In the solution process of the IHB method, the bounded parameters are considered as an active increment. Taking all values over the considered bounded regions of the active parameters provides us with a series of IHB solutions of limit cycle oscillations of the airfoil. With the aid of the attained solutions, the bounds and some statistical properties of the limit cycle oscillations are determined and compared with Monte Carlo simulation (MCS) results. Numerical examples show that the proposed approach is valid and effective for analyzing strongly nonlinear vibration problems with bounded uncertainties.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
34C46 Multifrequency systems of ordinary differential equations
65C05 Monte Carlo methods
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
74H50 Random vibrations in dynamical problems in solid mechanics
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