High frequency reduced models for repetitive beams. (2017)

• Record Type: Journal Article
• Authors: Rallu, Antoine; Hans, Stephane; Boutin, Claude
• Is Part Of: Procedia engineering. Volume 199(2017)
• Page Start: 1501
• Page End: 1506
• Publication Date: 2017
• Subjects: Periodic media -- reticulated beam -- modulation -- high frequency -- wave propagation -- multi-scale method; Engineering -- Congresses; Engineering -- Periodicals; Engineering; Conference proceedings; Periodicals; 620.005
• DOI: 10.1016/j.proeng.2017.09.487
• Languages: English
• ISSNs: 1877-7058

Abstract

Abstract: This work investigates high frequencies phenomena of large correlation length in periodic reticulated elastic media. In elasto-dynamics, the classical framework of homogenization of periodic media is based upon the principle of scale separation expressed on the motion, which is satisfied if the vibration wavelength is large compared to the cell dimension. Considering higher frequencies leads to introduce local dynamics state in the cell and therefore to lose the scale separation on the motion. However another kind of scale separation rises when the amplitude of the local periodic mode presents a large modulation length. Then an asymptotic procedure can be used, leading to the analytical equation describing the modulation. This method, applied first on a 1D spring-mass system then on reticulated beams, allows to establish modulation equations of various natures according to the multiplicity of the mode and to the number of cells on which the periodic mode is defined.