Design of Locally Resonant Acoustic Metamaterials with Specified Band Gaps Using Multi-Material Topology Optimization

Area of Science:

• Acoustics
• Materials Science
• Topology Optimization

Background:

• Locally Resonant Acoustic Metamaterials (LRAMs) offer potential for subwavelength band gaps.
• Current research often lacks methods for designing LRAMs with specific, targeted band gaps crucial for practical applications.

Purpose of the Study:

• To develop a parameterized level-set-based topology optimization method for designing multi-material LRAMs with specified frequency band gaps.
• To enable precise control over LRAM properties for applications requiring targeted frequency attenuation.

Main Methods:

• A parameterized level-set-based topology optimization framework utilizing multiple materials.
• A simplified band-gap calculation using a homogenization framework with restricted and unrestricted subsystems, avoiding Brillouin zone reliance.
• A multi-material representation model employing combinatorial level-set functions for efficient material transitions.

Main Results:

• Demonstrated effectiveness in designing LRAMs with specified band gaps using three- and four-material examples.
• Successfully addressed optimization problems including maximizing band-gap width within a frequency range and designing lightweight LRAMs with target band gaps.
• Validated the method's capability to achieve desired frequency constraints in LRAM design.

Conclusions:

• The proposed method offers a powerful tool for designing LRAMs with precisely controlled band gaps.
• This approach holds significant promise for developing advanced metamaterials for effective attenuation of specific frequency spectra, such as mechanical vibrations and environmental noise.