Measurement of vibrations of composite wings using high-order finite element beam

The purpose of this study is to show the influence of bending-torsion coupling on natural frequencies and mode shapes of aircraft wings by using two finite element beam formulations. The bending-torsion coupling parameters are the geometric parameter (distance between the mass axis and elastic axis of the cross-section of the beam) and the material coupling due to laminated composites. Cubic and high-order Hermite finite element interpolations are presented in this study, in order to show the influence of geometric and material coupling on natural frequencies and mode shapes. Starting by the governing partial differential equations of motion for the coupled bending-torsion beam with the bending and torsion equations, the Galerkin's method is used with high-order finite element interpolation to obtain the high-order Hermitian shape functions. The mass and stiffness matrices are obtained using the kinetic energy and potential energy, respectively. The beam finite element has two nodes, the cubic element has three degrees of freedom at each end (transvers displacement, slope and torsion), where the high order element has five degrees of freedom at each end (transvers displacement, slope, curvature, gradient of curvature and torsion). The mass matrix contains geometric coupling terms and the stiffness matrix contains terms of material bending-torsion coupling. The obtained results using cubic and high-order finite element Euler-Bernoulli beam formulations are compared for a free vibration analysis of Goland metallic wing (geometric coupling) and validated with Dynamic Stiffness Method for composite wings.