Structural nonlinearity is then modeled by a cubic nonlinear spring, since structures commenly behave as a cubic stiffness hardening spring. In flutter analysis the structure is, therefore, usually modeled by rigid airfoil mass-spring systems for wing structures and by plate equations for plate-like designs. This computationally highly intensive approach is usually too expensive for performing many deterministic simulations required in a flutter analysis study. Compared to the deterministic case the stochastic bifurcation can lead to an earlier onset of unstable flutter behavior, which can cause fatigue damage and structural failure.įluid-structure interaction systems can be modeled deterministically using detailed finite-element method (FEM) structural discretizations and high-fidelity unsteady computational fluid dynamics (CFD) simulations. Physical uncertainties are encountered in this kind of fluid-structure systems due to varying atmospheric conditions, wear and tear, and production tolerances affecting material properties and the geometry.
In this paper, the aeronautical application of the effect of randomness on the bifurcation of a nonlinear aeroelastic wing structure is analyzed. Stochastic parameters also affect the voltage oscillations in the electric circuit of a nonlinear transistor amplifier. The inherent sensitivity of meteorological and atmospheric models for weather prediction results in a rapid loss of simulation accuracy over time. In turbulence modeling and nonlinear stability theory of transition it is recognized that uncertainty in the initial conditions has a substantial effect on the long-term solution. Examples of significant effects of varying initial conditions and model parameters in time-dependent problems can be found in many branches of science and engineering. It is widely know that the behavior of nonlinear dynamical systems is highly sensitive to small variations. Disregarding seemingly less important random parameters based on a preliminary analysis can, therefore, be an unreliable approach for reducing the number of relevant random input parameters. The clear hierarchy of increasing importance of the random nonlinearity parameter, initial condition, and natural frequency ratio, respectively, even suddenly reverses. In this isolated point in parameter space The numerical results demonstrate that the system is even more sensitive to randomness at the higher period bifurcation than in the first bifurcation point. The robustness of the method is assured by the extrema diminishing concept in probability space.
The computationally efficient numerical approach achieves a constant error with a constant number of samples in time. Using an efficient and robust uncertainty quantification method for unsteady problems. The higher period stochastic bifurcation of a nonlinear airfoil fluid-structure interaction system is analyzed