Designing a phononic crystal with a defect for target frequency matching using an analytical approach

Abstract

This paper proposes a one-dimensional, defect-introduced phononic crystal design for target frequency matching. A quarter-wave stack is used as a unit cell. The supercell-technique-based transfer matrix method enables the defect’s length to be explicitly derived; this generates a defect band at the target frequency in band-structure analysis. For the verification through time-harmonic analysis, the perturbation-theory-incorporated S-parameter method is used. The results show that the proposed design enables the realization of defect-mode-induced energy localization at the desired frequency, regardless of the harmonic number, supercell size, and defect location. The proposed design is validated by numerical examples through the finite element method.

Keywords:

• Phononic crystal
• phononic band gap
• defect band
• energy localization
• target frequency matching
• transfer matrix method
• S-parameter method
• perturbation theory

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement

The data that supports the findings of this study are available within the article.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. 2020R1A2C3003644).