Mathematical singularity in the band structure calculations for phononic crystal with rigid scatterers (Conference Presentation)

Dmitrii Shymkiv; Arkadii Krokhin

doi:10.1117/12.2658509

12 June 2023 Mathematical singularity in the band structure calculations for phononic crystal with rigid scatterers (Conference Presentation)

Dmitrii Shymkiv, Arkadii Krokhin

Author Affiliations +

Proceedings Volume 12488, Health Monitoring of Structural and Biological Systems XVII; 1248811 (2023) https://doi.org/10.1117/12.2658509
Event: SPIE Smart Structures + Nondestructive Evaluation, 2023, Long Beach, California, United States

Abstract

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.

Conference Presentation

Citation Download Citation

Dmitrii Shymkiv and Arkadii Krokhin "Mathematical singularity in the band structure calculations for phononic crystal with rigid scatterers (Conference Presentation)", Proc. SPIE 12488, Health Monitoring of Structural and Biological Systems XVII, 1248811 (12 June 2023); https://doi.org/10.1117/12.2658509

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

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.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available