Multiscale Modeling of Wave Propagation in Viscoelastic Phononic Crystals and Acoustic Metamaterials
US National Science Foundation
Ruize Hu and Caglar Oskay
Phononic crystals and acoustic metamaterials exhibit extraordinary capability in controlling
acoustic and elastic waves by manipulating band gaps that forbid waves to propagate within
targeted frequency ranges.
Modeling of transient wave propagation in these composites using direct numerical simulations is computationally prohibitive for structural design and analysis.
- Develop a multiscale computational framework for efficient modeling of transient wave propagation in periodic viscoelastic composites, capturing wave dispersion and bandgap phenomenon.
Investigate the effects of microstructural morphology, elastic and viscoelastic constituent material properties on the overall wave attenuation behavior.
Spatial-temporal nonlocal homogenization model (STNHM)
High order asymptotic expansion
- Critical in extending the classical homogenization theory to short wavelength regime.
- Introduce spatial nonlocal terms in momentum balance equations at successive orders.
Construction of gradient-type nonlocal governing equation
- Derive temporal nonlocal terms in high symmetry directions of the first Brillouin zone.
- Nonlocal model parameters are uniquely determined by minimization of asymptotic residual.
Nonlocal effective medium model (NEM)
- Governing equation in the second order form with nonlocal features retained by the frequency-dependent nonlocal effective moduli tensor.
- Simulation of transient wave propagation without need of high order boundary conditions.
- Captures the acoustic branch, the stop band and the first optical branch in high symmetry directions.
- Evanescent wavenumber is predicted within the stop band.
Anti-plane shear wave
Transient wave propagation
In-plane elastic waveguide modeling
- Wave dispersion occurs at relatively low frequency.
- Highly confined wave propagation when wave frequency is within the stop band.
Anti-plane shear wave propagation in viscoelastic phononic crystal
- Nearly complete attenuation due to band gap formation and viscoelastic dissipation.
- Stronger attenuation compared to elastic phononic crystal.
- Compared to having viscoelastic dissipation only (LHM), band gap formation significantly improves wave attenuation.
- Layered microstructure has wider stop band and stronger wave attenuation within the stop band.