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.