Limit Cycle Oscillations (LCO) and Nonlinear Aeroelastic Wing Response: Reduced Order Aerodynamic Models

1999 ◽  
Author(s):  
Earl H. Dowell
Keyword(s):  
Limit Cycle ◽  
Limit Cycle Oscillations ◽  
Reduced Order

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and Its Application to Bladed Disks With Shroud Contact

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Christian Siewert ◽  
Andreas Hartung
Keyword(s):  
Limit Cycle ◽  
Large Scale ◽  
Computational Effort ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Reduced Order Model ◽  
Limit Cycle Oscillations ◽  
Order Model ◽  
Reduced Order ◽  
Modal Properties

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the multiharmonic balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary, e.g., for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using the generalized Fourier-Galerkin method. In order to efficiently study localized nonlinearities in large-scale systems, an exact condensation approach as well as analytically calculated gradients are employed. Moreover, a continuation method is employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the single nonlinear resonant mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for recomputation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. Forced response functions, backbone curves for varying normal preload, and excitation level as well as flutter-induced limit cycle oscillations are analyzed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

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