Advanced Beam Formulations for Free-Vibration Analysis of Conventional and Joined Wings

Abstract

This work extends advanced beam models to carry out a more accurate free-vibration analysis of conventional (straight, or with sweep/dihedral angles) and joined wings. The beam models are obtained by assuming higher-order (up to fourth) expansions for the unknown displacement variables over the cross-section. Higher-order terms permit bending/torsion modes to be coupled and capture any other vibration modes that require in-plane and warping deformation of the beam sections to be detected. Classical beam analyses, based on the Euler-Bernoulli and on Timoshenko beam theories, are obtained as particular cases. Numerical solutions are obtained by using the finite element (FE) method, which permits various boundary conditions and different wing/section geometries to be handled with ease. A comparison with other shell/solid FE solutions is given to examine the beam model. The capability of the beam model to detect bending, torsion, mixed and other vibration modes is shown by considering conventional and joined wings with different beam axis geometries as well as with various sections (compact, plate-type, thin-walled airfoil-type). The accuracy and the limitations of classical beam theories have been highlighted for a number of problems. It has been concluded that the proposed beam model could lead to quasi-three-dimensional dynamic responses of classical and nonclassical beam geometries. It provides better results than classical beam approaches, and it is much more computationally efficient than shell/solid modeling approaches.