Evaluation of continuous modelings for the modulated vibration modes of long repetitive structures

The aim of this paper is to evaluate a recently proposed continuous modeling for the modulated vibrations modes of long periodic structures. We describe an asymptotic two-scale method to study free vibrations of this type of structures in two cases: beam bending theory and 2D elasticity. A validation of the two proposed continuous modelings is presented and a comparison between 1D and 2D approach is given.