Decomposition-assisted analysis of transmission in periodic resonator arrays using mode-matching method

Area of Science:

• Acoustics
• Wave Propagation
• Materials Science

Background:

• Analyzing acoustic structures with locally reacting resonators is crucial for understanding sound scattering and transmission.
• Existing models face challenges in predicting sound propagation through non-uniform periodic resonator arrays.

Purpose of the Study:

• To develop an analytical framework for analyzing sound properties in periodic resonator arrays.
• To introduce a model for the input surface impedance of non-uniform resonator arrays.
• To simplify the analysis of sound transmission through these complex structures.

Main Methods:

• Employed a mode-matching method within a one-dimensional periodic structure.
• Decomposed the system into symmetric and antisymmetric sub-systems for simplified solutions.
• Verified the analytical model's accuracy through numerical simulations.

Main Results:

• Achieved simplified analytical solutions for transmission problems in non-uniform resonator arrays.
• Gained insights into mode shapes and amplitudes, complementing traditional acoustic parameters.
• Demonstrated the model's ability to predict transmission behavior and performance characteristics.

Conclusions:

• The proposed analytical method effectively models sound transmission in periodic varying-height resonator arrays.
• This approach enhances the understanding of acoustic fields beyond conventional metrics.
• The findings have potential applications in diverse systems, including electromagnetic devices.