A New Dynamic Finite Element Formulation with Applications to Composite Aircraft Wings
This thesis presents a new dynamic finite element (DFE) formulation for the free vibration of composite wings modeled as beam assemblies. Implementing Euler- Bemoulli beam theory, the initially assumed uniform beam is modeled in a progressive manner to produce a complex tapered composite thin-walled wing. The DFE employs dynamic trigonometric shape functions (DTSF’s) to produce a single dynamic stiffness matrix containing both mass and stiffness properties. Then, the Wittrick-William root counting algorithm is used to solve the resulting non-linear eigenvalue problem. The effective stiffness of a flat fiberous composite beam is modeled using classical laminate theory. The effective stiffness of a thin-walled wing-box is achieved by employing a circumferentially asymmetric stiffness (CAS) configuration. The convergence of the DFE is significantly better as compared to other existing methods, the Finite Element Method (FEM) and the Dynamic Stiffness Matrix (DSM), particularly for complex elements and higher modes of free coupled vibration.