Frequency domain approach for probabilistic flutter analysis using stochastic finite elements
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Frequency domain approach for probabilistic flutter analysis using stochastic finite elements Sandeep Kumar . Amit Kumar Onkar
. Manjuprasad Maligappa
Received: 22 February 2019 / Accepted: 30 September 2019 Ó Springer Nature B.V. 2019
Abstract In this work, a stochastic finite element method based on first order perturbation approach is developed for the probabilistic flutter analysis of aircraft wing in frequency domain. Here, both bending and torsional stiffness parameters of the wing are treated as Gaussian random fields and represented by a truncated Karhunen–Loeve expansion. The aerodynamic load on the wing is modeled using Theodorsen’s unsteady aerodynamics based strip theory. In this approach, Theodorsen’s function, which is a complex function of reduced frequency, is also treated as a random field. The applicability of the present method is demonstrated by studying the probabilistic flutter of cantilever wing with stiffness uncertainties. The present method is also validated by comparing results with Monte Carlo simulation (MCS). From the analysis, it is observed that torsional stiffness uncertainty has significant effect on the damping ratio and frequency of the flutter mode as compared to bending stiffness uncertainty. The probability density functions of damping ratio and frequency using
S. Kumar A. K. Onkar (&) M. Maligappa Academy of Scientific and Innovative Research at CSIR National Aerospace Laboratories, HAL Airport Road, Kodihalli, Bengaluru 560017, India e-mail: [email protected] S. Kumar A. K. Onkar M. Maligappa Structural Technologies Division, National Aerospace Laboratories, HAL Airport Road, Kodihalli, Bengaluru 560017, India
perturbation technique and MCS are also discussed at various free stream velocities due to stiffness uncertainties. Furthermore, the flutter probability of the cantilever wing is studied by defining implicit limit state function in conditional sense on flow velocity for the flutter mode. Both perturbation and MCS are considered to study the flutter probability of the wing. From the cumulative distribution functions of flutter velocity, it is noticed that the presence of uncertainty in torsional rigidity lowers the predicted flutter velocity in comparison to uncertainty in bending rigidity. Keywords Perturbation approach MCS Random process K–L expansion Flutter probability
1 Introduction Aeroelasticity is the study of the effect of aerodynamic forces on elastic structures. The critical aeroelastic phenomena which have major concern in the design of air vehicles are Divergence and Flutter. Divergence is a steady state aeroelastic phenomenon related to the lift redistribution on lifting surfaces in which, excessive elastic deformation leads to unstable wing. Flutter is a dynamic aeroelastic instability phenomenon due to interaction of unsteady aerodynamic, inertial, and elastic forces which results in unstable self excited
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Meccanica
oscillations of lifting components (Fung [13]). Here, the powe
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