APPLICATION OF THE WAVE FINITE ELEMENT APPROACH TO THE STRUCTURAL FREQUENCY RESPONSE OF STIFFENED STRUCTURES F . Errico 1 , M . Ichchou 2 , S . DeRosa 1 and O. Bareille 2 1 pasta-lab, Laboratory for Promoting experiences in Aeronautical STructures and Acoustics Dipartimento di Ingegneria Industriale - Sezione Aerospaziale e-mail: fabr.errico@studenti.unina.it; sergio.derosa@unina.it 2 LTDS, Laboratoire de Tribologie et Dynamique des Systems Ecole Centrale de Lyon e-mail: mohamed.ichchou@ec-lyon.fr; olivier.bareille@ec-lyon.fr Keywords: Wave Finite Element, Stiffened Structures Dynamics, Wave-mode expansion 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. 1 Introduction One of the most used and appealing methods for solving problem concerning the dynamics of continuous structures is the finite element method (FEM). Typically used for modal/dynamic- response applications, this method enhances the operator to obtain information about the vibrational level from the model of the whole structure in every frequency range. However, in many engineering applications, high frequency vibrations become significant, in particular where sound transmission and loading have to be considered, such as in the cases, for example, of the transmission loss COMPDYN 2017 6 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.) Rhodes Island, Greece, 15–17 June, 2017 Available online at www.eccomasproceedia.org Eccomas Proceedia COMPDYN (2017) 470-483 © 2017 The Authors. Published by Eccomas Proceedia. Peer-review under responsibility of the organizing committee of COMPDYN 2017. doi: 10.7712/120117.5433.16878