2018/03/13 by Armand Wirgin, Wirgin, Armand
Computer Science · Engineering · #Acoustic Wave Phenomena Research #Advanced Mathematical Modeling in Engineering #Applied Physics (physics.app-ph) #Composite Material Mechanics #FOS: Physical sciences #Material Properties and Processing #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.1803.04717
openalex publication_date 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose to homogenize a periodic (along one direction) structure, first in\norder to verify the quasi-static prediction of its response to an acoustic wave\narising from mixing theory, then to address the question of what becomes of\nthis prediction at higher frequencies. This homogenization is treated as an\ninverse (parameter retrieval) problem, i.e., by which we: (1) generate\nfar-field (i.e., specular reflection and transmission coefficients) response\ndata for the given periodic structure, (2) replace (initially by thought) this\n(inhomgoeneous) structure by a homogeneous (surrogate) layer, (3) compute the\nresponse of the surrogate layer response for various trial constitutive\nproperties, (4) search for the global minimum of the discrepancy between the\nresponse data of the given structure and the various trial parameter responses\n(5) attribute the homogenized properties of the surrogate layer for which the\nminimum of the discrepancy is attained. The result is that: (i) at low\nfrequencies and/or large filling factors, the effective constitutive properties\nare close to their static equivalents, i.e., the effective mass density is the\nproduct of a factor related to the given structure filling factor with the mass\ndensity of a generic substructure of the given structure and the effective\nvelocity is equal to the velocity in the said generic substructure, 2) at\nhigher frequencies and/or smaller city filling factors, the effective\nconstitutive properties are dispersive and do not take on a simple mathematical\nform, with this dispersion compensating for the discordance between the ways\nthe inhomogeneous given structure and the homogeneous surrogate layer respond\nto the acoustic wave.\n