Here we report the results obtained for band structure calculations of phononic crystals with rigid scatterers using the plane-wave expansion method. A scatterer with infinite acoustic impedance is modeled by approaching either the mass density or the elastic modulus to infinity. It is shown, that in both cases the dispersion equation contains singular matrices. This singularity leads to the correct band structure in the case of infinite elastic modulus. However, in the limiting case of infinite density the dispersion equation becomes meaningless. We explain the mathematical reason for this drastic difference.
Reciprocity is a fundamental property related to T-symmetry of wave equation. Nonreciprocal acoustic transmission becomes possible in a nonlinear or in a moving medium. Viscous losses, which break T-symmetry, are not considered as a nonreciprocal factor. We demonstrate that transmission through a finite-length dissipative phononic crystal is nonreciprocal for asymmetric scatterers. Asymmetric transmission is known even for inviscid background. However, additional nonreciprocal contribution related to the vorticity mode is usually missing. For infinite dissipative phononic crystal we prove that the decay coefficients turn out to be equal for the opposite directions but the velocity remains nonreciprocal due to broken PT-symmetry.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.