Homogenized dynamic constitutive relation for Bloch-wave propagation in periodic composites: structure and symmetries

2012 ◽  
Author(s):  
Sia Nemat-Nasser ◽  
Ankit Srivastava
Keyword(s):  
Wave Propagation ◽  
Constitutive Relation ◽  
Bloch Wave ◽  
Periodic Composites

Effective Dynamic Constitutive Relations for 3-D Periodic Elastic Composites

2013 ◽  
Vol 1508 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Constitutive Relation ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Bloch Wave ◽  
Ensemble Averaging ◽  
Periodic Composites ◽  
Effective Dynamic ◽  
Elastic Composites

ABSTRACTCentral to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. Recent advances in the theory of dynamic homogenization have established the coupled form of the constitutive relation (Willis constitutive relation). This coupled form of the constitutive relation naturally emerges from ensemble averaging of the dynamic fields and automatically satisfies the dispersion relation in the case of periodic composites. Its importance is also notable due to its invariance under transformational acoustics. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.

Effective Dynamic Properties of Microstructured Heterogeneous Materials

2012 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Constitutive Equations ◽  
Effective Properties ◽  
Dynamic Properties ◽  
Effective Property ◽  
Bloch Wave ◽  
Periodic Composites ◽  
Effective Dynamic ◽  
Dynamic Effective Properties

Central to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. While the theory of static effective property calculations goes back about 60 years, progress in the actual calculation of dynamic effective properties for periodic composites has been made only very recently. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.

scholarly journals “Fuzzy Band Gaps”: A Physically Motivated Indicator of Bloch Wave Evanescence in Phononic Systems

Crystals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 66
Author(s):  
Connor D. Pierce ◽  
Kathryn H. Matlack
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Quantitative Measure ◽  
Bloch Wave ◽  
Phononic Crystals ◽  
Wave Transmission ◽  
Band Gaps ◽  
Dissipative Systems ◽  
Frequency Range ◽  
Wave Modes

Phononic crystals (PCs) have been widely reported to exhibit band gaps, which for non-dissipative systems are well defined from the dispersion relation as a frequency range in which no propagating (i.e., non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Various measures have been proposed to quantify the “evanescence” of frequency ranges and/or wave propagation directions, but these measures are not based on measurable physical quantities. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite PC from the infinite dispersion relation is elusive. In this paper, we propose an “evanescence indicator” for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed “fuzzy band gaps” due to the smooth (rather than abrupt) transition between evanescent and propagating wave characteristics. The indicator is capable of identifying polarized fuzzy band gaps, including fuzzy band gaps which exists with respect to “hybrid” polarizations which consist of multiple simultaneous polarizations. We validate the indicator using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals.

Elastic Wave Propagation in Open-Cell Foams

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Alireza Bayat ◽  
Stavros Gaitanaros
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Finite Size ◽  
Bloch Wave ◽  
Elastic Wave Propagation ◽  
Surface Evolver ◽  
Dynamic Simulations ◽  
Element Analysis ◽  
Open Cell ◽  
Open Cell Foams

This work examines elastic wave propagation phenomena in open-cell foams with the use of the Bloch wave method and finite element analysis. Random foam topologies are generated with the Surface Evolver and subsequently meshed with Timoshenko beam elements, creating open-cell foam models. Convergence studies on band diagrams of different domain sizes indicate that a representative volume element (RVE) consists of at least 83 cells. Wave directionality and energy flow features are investigated by extracting phase and group velocity plots. Explicit dynamic simulations are performed on finite size domains of the considered foam structure to validate the RVE results. The effect of topological disorder is studied in detail, and excellent agreement is found between the wave behavior of the random foam and that of both the regular and perturbed Kelvin foams in the low-frequency regime. In higher modes and frequencies, however, as the wavelengths become smaller, disorder has a significant effect and the deviation between regular and random foam increases significantly.

Highly controlled Bloch wave propagation in surfaces with broken symmetry

2018 ◽  
Vol 43 (11) ◽  
pp. 2660 ◽  
Author(s):  
Döne Yilmaz ◽  
Aydan Yeltik ◽  
Hamza Kurt
Keyword(s):  
Wave Propagation ◽  
Bloch Wave ◽  
Broken Symmetry

Fourier analysis of Bloch wave propagation in two-dimensional photonic crystals

2004 ◽  
Author(s):  
Benoit Lombardet ◽  
L. Andrea Dunbar ◽  
Rolando Ferrini ◽  
Romuald Houdre
Keyword(s):  
Wave Propagation ◽  
Photonic Crystals ◽  
Fourier Analysis ◽  
Bloch Wave ◽  
Two Dimensional

Design of Miura-Ori Patterns With Acoustic Bandgaps

2017 ◽  
Author(s):  
Phanisri P. Pratapa ◽  
Phanish Suryanarayana ◽  
Glaucio H. Paulino
Keyword(s):  
Wave Propagation ◽  
Material Properties ◽  
Bloch Wave ◽  
Acoustic Metamaterials ◽  
Analysis Framework ◽  
Wave Analysis ◽  
Material Inhomogeneity ◽  
Propagation Behavior ◽  
Unit Cells ◽  
Bloch Wave Analysis

We study the wave propagation behavior in Miura-ori patterns by using the Bloch-wave analysis framework. Our investigation focuses on acoustic bandgaps that act as stopping bands for wave propagation at certain frequencies in periodic solids or structures. We show that bandgaps can be created in two-dimensional periodic Miura-ori patterns by introducing material inhomogeneity. First, we perform Bloch-wave analysis of homogeneous Miura-ori patterns with finite panel rigidity and find that no bandgaps are present. We then introduce bandgaps by making the pattern non-uniform — by changing the mass and axial rigidity of origami panels of alternating unit cells. We discuss the dependence of the magnitude of the bandgap on the contrast between material properties. We find that higher magnitudes of bandgaps are possible by using higher contrast ratios (mass and stiffness). These observations indicate the potential of origami-based patterns to be useful as acoustic metamaterials for vibration control.

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