Prediction of Limit Cycle Oscillations Based on Dynamic Eigen Decomposition of Flight Test Data

ifasd2024 Tracking Number 232

During the design and test phases of aircraft structure, flutter boundaries are computed using analysis tools such as the p-k iterations or eigenvalue analysis. Also, for the purpose of certification flight flutter test (FFT) is conducted to estimate the critical aeroelastic damping and predict the onset of flutter experimentally. However, from the practical perspective Limit Cycle Oscillation (LCO) which is referred to as an aeroelastic vibration with a finite amplitude is more critical because it represents not only the true nonlinear nature of the fluid-structure interaction but also the potentially more dangerous dynamic instability that could occur at speeds lower than the flutter point. Previously, based on the concept of the Dynamic Eigen Decomposition (DED) and a frequency domain stability theorem, a new theory of flutter prediction was developed [1] and modified for applications to FFT with limited actuators and sensors [2]. In the present work, the original techniques are extended and modified to account for the large amplitude LCOs. For this initial work, we will focus on the structural nonlinearity caused by the control surface free-play, assuming that aerodynamically the system remains dynamically linear. It will be shown that when a nonlinear solution is sought in a simple harmonic fashion similar to harmonic balance approach to general engineering problems, the LCO can be interpreted as a dynamic instability with zero effective damping. Thus, as in the linear flutter prediction an LCO can be found by checking the dynamic eigenvalues λ(ω)’s in the frequency domain with an effective control surface stiffness. First, harmonic excitations of the control surface are carried out at discrete frequencies at several subcritical flight conditions. Next, using the data a new DED is formulated combining the two oscillation cases in two parameters, i.e., the variable dynamic pressure Δq and variable stiffness of the control surface hinge ΔK: c_c [-ω^2 M+jωC+K+mΔK-(q_D+kΔq)Q(k)]^(-1) mb_c=v_t (k,ω) λ_t (k,m,ω) w_t (k,ω) where λ_t (k,m,ω)=m〖λ^'〗_t (k,ω)/(1-m〖λ^'〗_t (k,ω)) and 〖λ'〗_t (k,ω)’s are dynamic eigenvalues when only the dynamic pressure changes. With the new formulation one can iterate on k and m, i.e., dynamic pressure and the control surface amplitude until a LCO point is found. This procedure is very similar to the procedure of linear flutter prediction except that we now have two, instead of one, parameters. The essential characteristic of the nonlinear aeroelastic LCO phenomena that there exists one-to-one relation between the amplitude of the oscillation and dynamic pressure is well captured. Most importantly, only a single excitation and a single sensor are required, and this is very desirable for LCO prediction based on experimental data from wind tunnel or flight tests. Furthermore, no extra flight tests are necessary beyond the regular flutter tests. For the upcoming IFASD paper, the proposed scheme will be demonstrated using computational simulations of a tapered straight wing with four flaps along the trailing edge. Should FFT data be available, LCO prediction results based on the experimental data will be also included and reported. References [1] Kim, T., Flutter Prediction Methodology Based on Dynamic Eigen Decomposition and Frequency-Domain Stability, Journal of Fluids and Structures 2019; 86; 0-13. [2] Kim, T., Progressive Flutter Prediction Using Flight Data with Limited Sensors and Actuators, SciTech, January 8-12, 2024, Orlando, FL, USA.