• Corpus ID: 239016630

Bloch Spectra for High Contrast Elastic Media

  title={Bloch Spectra for High Contrast Elastic Media},
  author={Robert P. Lipton and Ruchira Perera},
Analytic representation formulas and power series are developed to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lamé system inside phononic crystals. Convergent power series for the Bloch wave spectrum are obtained using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the… 

Figures from this paper


Bloch Waves in Crystals and Periodic High Contrast Media
Analytic representation formulas and power series are developed describing the band structure inside periodic photonic and acoustic crystals made from high contrast inclusions. Central to this
Asymptotic Analysis of High-Contrast Phononic Crystals and a Criterion for the Band-Gap Opening
We investigate the band-gap structure of the frequency spectrum for elastic waves in a high-contrast, two-component periodic elastic medium. We consider two-dimensional phononic crystals consisting
Creating Band Gaps in Periodic Media
The theory provides a systematic means for the identification of photonic and phononic band gaps within a specified frequency range and provides an accurate characterization of the quasi-periodic and electrostatic resonance spectrum.
Spectral properties of periodic media in the large coupling limit
We investigate the band­gap structure and the integrated density of states for a class of periodic divergence type operators which, in the simplest case, are given by , acting in . We assume here
Multiscale Modeling of Elastic Waves: Theoretical Justification and Numerical Simulation of Band Gaps
It is shown how to compute the existence of forbidden bands, i.e., intervals of frequencies in which there is no propagation of elastic waves, and illustrated the theoretical results with some numerical simulations.
Numerical simulation of acoustic band gaps in homogenized elastic composites
Abstract The dispersion of acoustic or elastodynamic waves in elastic composites are studied using the homogenized model. We consider heterogeneous periodic structures consisting of soft but heavy
Spectral properties of the Neumann–Poincaré operator and cloaking by anomalous localized resonance for the elasto-static system
We first investigate spectral properties of the Neumann–Poincaré (NP) operator for the Lamé system of elasto-statics. We show that the elasto-static NP operator can be symmetrized in the same way as
Homogenization Approach and Bloch-Floquet Theory for Band-Gap Prediction in 2D Locally Resonant Metamaterials
This paper provides a detailed comparison of the two-scale homogenization method and of the Bloch-Floquet theory for the determination of band-gaps in locally resonant metamaterials. A medium
Shape optimization of phononic band gap structures using the homogenization approach
Abstract The paper deals with optimization of the acoustic band gaps computed using the homogenized model of strongly heterogeneous elastic composite which is constituted by soft inclusions
Elastostatic resonances—a new approach to the calculation of the effective elastic constants of composites☆
Abstract A new method is presented for a systematic evaluation of the effective elastic tensor C (e) in a two-component composite. Both C (e) and local strain field are expanded in terms of a