Flutter analysis of fixed and rotary wings through a one-dimensional unified formulation

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.