Metamaterials in musical acoustics: A modified frame drum

Abstract

Acoustic metamaterials have properties not found in nature, like negative stiffness, cloaking behavior or frequency bandgap damping. This is achieved by complex geometries often constructed out of multiple subunits in sub-wavelength size. Although also musical instruments often have complex shapes, like guitar or piano soundboards with regular fan bracing, metamaterials have not explicitly been used here. As an example, a modified frame drum is proposed with increased sound possibilities by adding masses to the drum membrane arranged in a circle. Such structures have been shown to have cloaking behavior. Using microphone-array and laser interferometry measurements it is shown that such a drum has a frequency-dependent cloaking behavior. When struck at the center of the added circle most energy above about 400 Hz stays in the circle and decays strongly. Such a sound cannot be produced with a regular frame drum. When struck outside the circle the drum sounds very much like a regular drum without added masses. By gradually changing the playing position from the circle center towards the circle rim, frequencies above about 400 Hz are gradually added. Therefore such a modified frame drum has much more possible sounds and therefore ways of musical articulation.