Multiscale Modeling of Elastic Waves: Theoretical Justification and Numerical Simulation of Band Gaps
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Summary
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.
- Type
- article
- Published
- 2008-04-11
- Cited by
- 65
- References
- 16
- Access
- Open access
- OpenAlex
- https://openalex.org/W1990947082
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:27957068
Keywords
Long wavelength limit, Homogeneous, Elasticity (physics), Limit (mathematics), Physics
References
- Periodic unfolding and homogenization
- Derivation of the double porosity model of single phase flow via homogenization theory
- Bandes phononiques interdites en élasticité linéarisée
- Systematic design of phononic band–gap materials and structures by topology optimization
- Photonic Band Structures
- Photonic band-gap crystals
- Homogenization and two-scale convergence
- On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases
- Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media
- Theory of mesoscopic magnetism in photonic crystals.
- Homogenization near resonances and artificial magnetism from dielectrics
- A general convergence result for a functional related to the theory of homogenization
- Magnetism from conductors and enhanced nonlinear phenomena
- Negative refraction in periodic and random photonic crystals
Cited by
- Two-Scale Homogenisation of Partially Degenerating PDEs with Applications to Photonic Crystals and Elasticity
- Quelques modèles mathématiques homogénéisés appliqués à la modélisation du parenchyme pulmonaire
- Wave propagation and band gaps in homogenized phononic plates — modelling by spectral decomposition
- On acoustic band gaps in homogenized piezoelectric phononic materials
- Numerical simulation of acoustic band gaps in homogenized elastic composites
- Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization
- Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions
- Modelling and sensitivity analysis for design of phononic crystals
- Trampoline metamaterial: Local resonance enhancement by springboards
- Homogenization of the 3D Maxwell system near resonances and artificial magnetism
- Homogenization of acoustic waves in strongly heterogeneous porous structures
- Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook
- Homogenization of a Model for the Propagation of Sound in the Lungs
- Band gaps and vibration of strongly heterogeneous Reissner–Mindlin elastic plates
- Second-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limits
- Modelling response of phononic Reissner-Mindlin plates using a spectral decomposition
- Homogenization of transmission conditions for analysis of acoustic waves in domains with perforated barriers
- Homogenization of the acoustic transmission through a perforated layer
- Multiscale Modeling of Weakly Compressible Elastic Materials in the Harmonic Regime and Applications to Microscale Structure Estimation
- Homogenization of materials with sign changing coefficients
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