English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the propagation of acoustic time-harmonic waves in a homogeneousmedia containing periodic lattices of spherical or cylindrical inclusions. Itis assumed that the wavelength has the order of the periods of the latticewhile the radius $a$ of inclusions is small. A new approach is suggested toderive the complete asymptotic expansions of the dispersion relations in twoand three-dimensional cases as $a \to 0$ and evaluate explicitly several firstterms. Our method is based on the reduction of the original singularlyperturbed (by inclusions) problem to the regular one. The Neumann, Dirichletand transmission boundary conditions are considered. The effective wave speedis obtained as a function of the wave frequency, the filling fraction of theinclusions, and the physical properties of the constituents of the mixture.Dependence of asymptotic formulas obtained in the paper on geometric andmaterial parameters is illustrated by graphs.

Dispersion of waves in two and three-dimensional periodic media