An inverse procedure for determination of material constants of a periodic multilayer using Floquet wave homogenization

Dispersion curves play a relevant role in nondestructive testing. They provide estimations of the elastic and geometrical parameters from experiments and offer a better perspective to explain the wave field behavior inside bodies. They are obtained by different methods. The Floquet-Bloch theory is presented as an alternative to them. The method is explained in an intuitive manner; it is compared to other frequently employed techniques, like searching root based algorithms or the multichannel analysis of surface waves methodology, and finally applied to fit the results of a real experiment. The Floquet-Bloch strategy computes the solution on a unit cell, whose influence is studied here. It is implemented in commercially finite element software and increasing the number of layers of the system does not bring additional numerical difficulties. The lateral unboundedness of the layers is implicitly taken care of, without having to resort to artificial extensions of the modelling domain designed to produce damping as happens with perfectly matched layers or absorbing regions. The study is performed for the single layer case and the results indicate that for unit cell aspect ratios under 0.2 accurate dispersion curves are obtained. The method is finally used to estimate the elastic parameters of a real steel slab.

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“…From (9) and (11), the solution of the problem will be equivalent if the wave vector and the F-B exponent FB are related as…”

Section: Floquet-bloch Theory and Guided Waves In Layersmentioning

confidence: 99%

“…There, the physical periodic structure of the studied object translates into spatial periodicity of its coefficients. Therefore, the F-B theory has been applied to obtain the dispersive properties of different mechanical periodic systems [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Floquet-Bloch Theory and Its Application to the Dispersion Curves of Nonperiodic Layered Systems

García

Fernández-Álvarez

2015

Mathematical Problems in Engineering

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“…Here the physical periodic structure of the object under study translates into the periodicity of its coefficients. Therefore, Floquet-Bloch theory has found different applications to study and investigate the distribution properties of different mechanical periodic systems [5], [6]. Many structures, mostly civil engineering structures [2], [3], optical [10], [11], or electromagnetic [12], can be considered as infinitely large layered systems.…”

Section: Introductionmentioning

confidence: 99%

Floquet Bloch Theory Used to Analyze the Stability of Periodic Systems

2023

Proceeding Book of 3rd International Conference on Scientific and Academic Research ICSAR 2023

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This study, the role and effects of Floquet Bloch theory on partial differential equations with periodic coefficients were investigated. Results are given about the Floquet expansions of arbitrary solutions, the solvability of non-homogeneous equations, the existence and structure of solutions, especially for boundary value problems that arise in applications of Schrödinger equations. This theory is of great importance for the quantum theory of solids, the theory of waveguides, scattering theory and other fields of mathematical and theoretical physics.

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Observance of Stoneley waves at the Lamb wave dispersion in stratified media

Kuznetsov

2019

Arch Appl Mech

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An inverse procedure for determination of material constants of a periodic multilayer using Floquet wave homogenization

Cited by 8 publications

References 9 publications

Floquet-Bloch Theory and Its Application to the Dispersion Curves of Nonperiodic Layered Systems

Floquet-Bloch Theory and Its Application to the Dispersion Curves of Nonperiodic Layered Systems

Floquet Bloch Theory Used to Analyze the Stability of Periodic Systems

Observance of Stoneley waves at the Lamb wave dispersion in stratified media

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