Probabilistic Flutter Analysis of a Cantilever Wing
A probabilistic flutter analysis of geometrically coupled cantilever wing is carried out using first-order perturbation approach by considering bending and torsional rigidities as Gaussian random variables. The unsteadiness in the aerodynamic flow is mode
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Abstract A probabilistic flutter analysis of geometrically coupled cantilever wing is carried out using first-order perturbation approach by considering bending and torsional rigidities as Gaussian random variables. The unsteadiness in the aerodynamic flow is modeled using Theodorsen’s thin airfoil theory. The probabilistic response of the wing is obtained in terms of mean, standard deviation, and coefficient of variation (COV) of real and imaginary parts of the eigenvalues at various free stream velocities. The perturbation results are also compared with Monte Carlo simulations. It is observed that the probabilistic response obtained from the perturbation approach is very accurate up to 7% COV in bending rigidity but in the case of torsional rigidity, it starts losing accuracy after 3%. Keywords Probabilistic flutter · Perturbation · MCS · Goland wing
1 Introduction In the design of aircraft, one of the critical failure phenomena, which happens in the aeroelastic system due to the fact that power pumped by aerodynamic flow is not completely able to be dissipated by the dissipative mechanism of the aeroelastic system, and the structure fails catastrophically due to diverging large amplitude vibrations. The flow velocity at which there is power balance, is called flutter velocity. In general, the material properties of the structure is not unique, and it depends on various factors such as method of manufacturing, method of testing and S. Kumar · A. K. Onkar (B) · M. Manjuprasad Academy of Scientific and Innovative Research (AcSIR), Bengaluru 560017, Karnataka, India e-mail: [email protected] S. Kumar e-mail: [email protected] M. Manjuprasad e-mail: [email protected] CSIR-National Aerospace Laboratories, Bengaluru 560017, Karnataka, India © Springer Nature Singapore Pte Ltd. 2021 S. Dutta et al. (eds.), Advances in Structural Vibration, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-5862-7_12
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test conditions, human errors in calculation, etc. So the material properties must be modeled as stochastic parameters in order to get more realistic results. Pettit [1] showed the importance and challenges of uncertainty quantification in aeroelasticity and potential future application of uncertainty-based aircraft design over the conventional factor of safety-based design. Kurdi et al. [2] considered the box type of Goland wing with spars and ribs, and their thickness and area were considered as Gaussian random variables. For probabilistic response analysis, a Monte Carlo Simulation (MCS) approach was used where free vibration and flutter analyses were conducted using MSC-Nastran and ZONA 6 module of ZAERO, respectively. Khodaparast et al. [3] used Nastran-based doublet lattice method for aerodynamic modeling to carry out both probabilistic and non-probabilistic flutter analysis of aircraft wing. The wing with spar, ribs, upper and lower skins, and their thickness and area were considered as random variables. For probabilistic analysis, perturbation met
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