Abstract
Carrera Unified Formulation (CUF) is used to perform flutter analyses of fixed and rotary wings. The one-dimensional refined theories are obtained through an axiomatic enrichment of the displacement field components by only setting the input parameters, namely the number of terms and the kind of the cross-sectional functions. Within this work, Taylor-like expansions of N-order (TEN) are used. The aerodynamic loadings are determined through the unsteady strip theories proposed by Theodorsen and Loewy. The finite element method is used to solve the governing equations that are derived, in a weak form, using the generalized Hamilton’s Principle. These equations are written in terms of CUF “fundamental nuclei”, which do not vary with the theory order (N). The flutter instability of fixed and rotary wings with rectangular and realistic cross-sections is investigated. The results are reported in terms of flutter velocities and frequencies and, when possible, they are compared with experimental, numerical and analytical solutions. Despite the intrinsic limitations of the used aerodynamic theories, the proposed methodology appears valid for aeroelastic and vibrational analyses of several structures by ensuring a significant accuracy with a low computational cost.
Highlights
According to Collar’s definition, aeroelasticity is ‘‘the study of the mutual interaction that takes place within the triangle of the inertial, elastic, and aerodynamic forces acting on structural members exposed to an air stream, and the influence of this study on design’’
The rapid increase of the computational power has motivated the development in the area of computational fluid dynamics (CFD)
Over the last 30 years, the CFD based aeroelasticity progressed from full potential theo ries to problems governed by the Navier Stokes equations
Summary
According to Collar’s definition, aeroelasticity is ‘‘the study of the mutual interaction that takes place within the triangle of the inertial, elastic, and aerodynamic forces acting on structural members exposed to an air stream, and the influence of this study on design’’. Other valuable models were proposed on the basis of Greenberg’s theory [24], where a pulsating velocity varia tion and a constant pitch angle were included in Theodorsen’s model These modifications were extended to the case of rotary wings in [25], in which Theodorsen’s, Loewy’s and Poisso’s theories were used for studying the flap lag torsional coupling. The authors pointed out that the above modifications should be included to realistically reproduce the aeroelasticity of rotary wings, where the assumptions commonly used in deriving strip theories (1 cross sections are assumed to perform only simple harmonic pitching and plunging oscillations about a zero equilibrium posi tion; 2 the velocity of oncoming airflow is constant; 3 usual potential small disturbance unsteady aerodynamics are assumed to apply) are intrinsically violated. Aeroelastic analyzes were performed on fixed wing configurations by combining the TE elements with aerodynamic panel methods [48,49] and unsteady strip theories [50]
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