Expanding the design space and optimizing stop bands for mechanical metamaterials

Abstract

A predictive design, analysis, and optimization tool that quickly and accurately captures the frequency response of locally resonant metamaterials is presented. A reduced order model based on a discrete spring-mass system is used to relate the structural parameters of a unit cell to frequency response, intended for optimizing for the unit cell structure with the widest longitudinal stop band at a desired center frequency. Design maps that relate geometric parameters to performance metrics are assembled, from which optimized unit cells or paths for enhanced functionality can be identified. The method can be augmented to examine all vibration modes or extended to multi-dimensional wave propagation, such as shear or oblique waves. The practicality of the design maps is demonstrated through two examples. First, actual 3D printed size and material limitations are imposed onto the design maps to bound a physically realizable design space. The identified optimal geometry has the maximum gap width at the desired center frequency within the bounds. The second example utilizes tunable, filled resin systems to expand the design space through material variations. Multi-material unit cells fabricated with frames and resonators having different material properties are predicted to provide better performance than cells consisting of a single material.

Keywords

• Mechanical metamaterial
• Reduced order model
• Additive manufacturing
• Stop band
• Optimization
• Acoustic