Comparison of dynamic stiffness and finite element methods in dynamics and aeroelastic response

In linear elasticity, most of the theories of structures in dynamics are governed by partial differential equations of motion. Among the others, the Finite Element Method (FEM) is a numerical technique aiming at solving the above problem by reducing it in a system of algebraic equations. Although being very popular, FEM suffers of some well-known problems and it is limited to the low-frequency range. An alternative method is the Dynamic Stiffness Method (DSM), which allows to solve the differential equations of motion in an exact manner with no numerical approximations. DSM has most of the FEM capabilities. However, unlike FEM, DSM brings to a transcendental non-linear eigenvalue problem and the algorithm by Wittrick and Williams, which is an iterative procedure, is needed to solve the frequency-dependant Dynamic Stiffness matrix. In this work, FEM and DSM are applied with reference to the Carrera Unified Formulation (CUF), which allows for the straightforward implementation of higher-order hierarchical beam theories without the need for ad hoc assumptions. Different structural problems are addressed, including metallic and composite lifting surfaces for free vibrations and aeroelastic response analyses. The results show the uncompromising accuracy of DSM in seeking the free vibration characteristics of the structures considered. On the other hand, it is demonstrated that FEM is sufficient for flutter analysis since aeroelastic phenomena only excite the first vibration modes.