Design of a 2D Plate Adaptable Metamaterial Unit Cell Using Finite Elements

Acoustic metamaterials are composite materials exhibiting effective properties and acoustic behavior not found in traditional materials. Through periodic subwavelength resonant inclusions, acoustic metamaterials enable steering, cloaking, lensing, and frequency band control of acoustic waves. A common drawback of acoustic metamaterials is that the properties are limited to narrow frequency bands. Investigation of practical active and adaptable acoustic metamaterials is valuable in achieving wider operation frequency bands. In this work, we explore different geometric configurations for a cutaway plate metamaterial unit cell with the purpose of vibration suppression. Resonators cut directly in a thin uniform plate function as local resonators. We examine the wavenumber band structure seeking wide and low frequency band gaps in the vicinity of the resonant frequencies of the local resonators. Variations in the geometry of the unit cell are examined to obtain band gaps for broadband vibration suppression. Wave shapes of the unit cell associated with the band gaps are also examined to aid in the parametric design of the unit cell. Additionally, as a means of tuning stiffness of the local resonators we attach piezoelectric actuators to the cutaway resonators with the goal of increasing the bandwidth of the vibration suppression and enabling frequency tunability of the system.