Diffusion based homogenization method for 1D wave propagation. (February 2020)

• Record Type: Journal Article
• Authors: Ahsani, S.; Boukadia, R.; Droz, C.; Claeys, C.; Deckers, E.; Desmet, W.
• Is Part Of: Mechanical systems and signal processing. Volume 136(2020)
• Publication Date: 2020-02
• Subjects: Periodic structures -- Homogenization -- Wave Finite Element Method -- Diffusion Matrix Model -- Coherent Potential Approximation; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2019.106515
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: Equivalent material properties calculation by exploiting WFEM in a CPA context. DMM to match the local scattering behavior of the equivalent and original medium. Good numerical agreement between the effective and original model on FRFs. Abstract: The implementation of increasingly complex periodic structures for vibro-acoustic purposes in civil engineering and transportation industry creates new modeling and computational challenges, mainly due to the multi-scale nature of the structures. Homogenization techniques able to describe the local dynamics effects appearing in periodic structures have therefore received significant attention in the past years. In this paper, a homogenization technique is proposed for 1D periodic media, where the equivalent material properties are determined using the local wave scattering characteristics of the periodic medium. A Wave Finite Element scheme is used to retrieve the multi-modal interface diffusion coefficients based on a unit-cell FE model of the periodic structure. The homogenized model is then used to derive wavenumbers and Frequency Response Function of the waveguide. Four examples are proposed, including a 3D periodic waveguide exhibiting locally resonant bandgaps. Good agreement is observed. Also limitations of the method are discussed.