Effective acoustic metamaterial homogenization based on Hamilton's principle with a multiple scales approximation

Area of Science:

• Acoustics
• Materials Science
• Applied Mathematics

Background:

• Acoustic metamaterials offer unique sound manipulation properties.
• Homogenization methods are crucial for understanding effective material behavior.
• Existing methods may lack versatility or struggle with complex physical effects.

Purpose of the Study:

• To derive and demonstrate a novel one-dimensional acoustic metamaterial homogenization method.
• To showcase the method's versatility in accounting for various physical phenomena.
• To provide a framework for analyzing complex acoustic metamaterial behavior.

Main Methods:

• Utilizes a multiple-scales approximation.
• Employs Hamilton's principle for a weak-form dynamic equation representation.
• Combines analytical and numerical approaches for validation.

Main Results:

• The derived homogenization method is demonstrated to be highly versatile.
• The method successfully accounts for viscosity effects in acoustic metamaterials.
• Finite-amplitude effects are also shown to be manageable with this technique.

Conclusions:

• The developed homogenization method provides a versatile tool for acoustic metamaterial analysis.
• The approach offers a pathway to understanding complex material properties.
• This method has potential applications in designing advanced acoustic devices.