APPLICATION OF THE WAVE FINITE ELEMENT APPROACH TO THE STRUCTURAL FREQUENCY RESPONSE OF STIFFENED STRUCTURES

The present work shows many aspects concerning the use of the wave methodology for the response computation of periodic structures, through the use of substructures and single cells. Applying Floquet principle, continuity of displacements and equilibrium of forces at the interface, an eigenvalue problem, whose solutions are the waves propagation constants and wavemodes, is defined. With the use of single cells, thus a double periodicity, the dispersion curves of the waveguide under investigation are obtained and a validation of the results is performed with analytic ones, both for isotropic and composite material. Two different approaches are presented, instead, for computing the forced response of stiffened structures, through substructures of the whole periodic structure. The first one, dealing with the condensed-to-boundaries dynamic stiffness matrix, proved to drastically reduce the problem size in terms of degrees of freedom, with respect to more mature techniques such as the classic FEM. Moreover it proved to be the most controllable one. The other approach presented deals with waves propagation and reflection in the structure. However it suffers more numerical conditioning and requires a proper choice of the reflection matrices to the boundaries, which has been one of the most delicate passages of the whole work, as the effects of the direct excitation. However this last approach can deal with the response and loads applied on any inner point. The results show a good agreement with numerical classic-FEM except for damping needed to be trimmed for perfect agreement . The drastic reduction of DoF is evident, even more when the number of repetitive substructures is high and the substructures itself is modelled in order to get the lowest number of DoF at the boundaries.