The article investigates a polyethylene-based metamaterial aimed at acoustic control, emphasizing the development of a relaxed micromorphic model. It discusses dispersion curves and the significance of analytical expressions for cut-offs and asymptotes, departing from traditional pointwise fitting methods. Further sections elaborate on the model's consistency concerning changes in unit cell properties and size, leading to important insights into the behavior of acoustic metamaterials. The findings underline the complexities of deriving asymptotes, showcasing their dependence on intricate polynomial solutions and providing a framework for future applications in acoustic engineering.
In the study of a polyethylene-based metamaterial, we utilized analytical expressions for cut-offs and asymptotes to understand dispersion curves better rather than pointwise fitting.
Our focus shifted towards deriving explicit expressions for both cut-offs and asymptotes by considering limits in various conditions, which revealed deeper insights into unit cell behavior.
The complexity of deriving asymptotes stems from the need to solve a third order polynomial, contrasting with the previous simpler cut-off calculations.
The relaxed micromorphic model's consistency with diverse unit cell properties and sizes emphasizes its robustness in acoustic metamaterials and their applications.
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