Vibration Analysis of Composite Wings Undergoing Material and Geometrical Couplings: A Dynamic Finite Element Formulation

Abstract

The differential equations governing Geometric-Materially coupled torsion-flexural vibrations of laminated composite wings are first reviewed. Based on the finite element methodology (FEM), Euler-Bernoulli and St-Venant beam theories, the Dynamic Trigonometric Shape Functions (DTSFs) for the beam’s uncoupled displacements are thereafter derived. Exploiting the Principle of Virtual Work (PVW) and interpolating the variables based on the DTSF, the Dynamic Finite Element (DFE) formulations for uniform beams’ coupled vibrations are first developed. The variable geometrical and mechanical parameters are then incorporated in the formulation. The applicability of the DFE method is then demonstrated by two illustrative examples where a Wittrick-Williams root counting technique is used to find the systems’ natural frequencies. The proposed DFE approach can also be advantageously extended to incorporate more complexities, further coupling as well as other geometrical and mechanical parameters in the formulation.