Asymptotic analysis of high-frequency modulation in periodic systems. Analytical study of discrete and continuous structures

High-frequency modulations in reticulated beams are then investigated. The dispersion equation for longitudinal and transversal vibrations are first established. Then, from the asymptotic analysis, the equations governing the structure behavior in the standard homogenization regime and in the modulation regimes are derived. These results are illustrated and supported by numerical simulations. General comments on modulation and potential application are developed in the conclusions.