Low-frequency wave-energy amplification in graded two-dimensional resonator arrays

Area of Science:

• Acoustics
• Wave Phenomena
• Materials Science

Background:

• Structured media, such as resonator arrays, can exhibit unique wave propagation properties.
• Understanding energy amplification in these systems is crucial for designing advanced acoustic devices.
• Previous studies have explored wave localization and manipulation in periodic structures.

Purpose of the Study:

• To investigate energy amplification in graded square-lattice arrays of C-shaped resonators.
• To analyze the phenomenon in both infinite and finite two-dimensional linear acoustic settings.
• To identify the underlying mechanisms and predict locations of significant energy amplification.

Main Methods:

• Band diagram analysis for doubly-periodic arrays.
• Numerical simulations of infinite and finite resonator arrays.
• Eigenvalue analysis of transfer matrices for individual array columns.

Main Results:

• Large energy amplifications were observed at specific locations within the resonator arrays.
• Propagation cut-offs in transfer-matrix eigenvalues accurately predict amplification sites in infinite arrays.
• Finite arrays exhibit complex amplification patterns due to multiple discrete modes, with single-row arrays showing the highest amplification.

Conclusions:

• The study demonstrates effective energy amplification in graded C-shaped resonator arrays.
• Transfer-matrix eigenvalue analysis provides a predictive tool for amplification locations.
• Array geometry, particularly finiteness and grading, significantly influences amplification characteristics.