Optimization of Natural Frequencies for Fabricable 3D Objects (DAAV)

  The advent of consumer-grade 3D printing has recently sparked interest in fabrication-aware shape optimization in order to further the potential of customized part production. An intrinsic property of every tangible object is its natural frequency spectrum, which controls its characteristic pitch and timbre when struck with a mallet.   We propose to use classical finite element analysis as part of an optimization framework that automatically modifies a given finite element mesh to exhibit a given natural frequency. Depending on the input geometry, we show how different element types are more suitable, and how different shape parameterizations can be applied.   Our algorithm is validated by fabricating objects and determining their predominant frequencies with a standard microphone. The musical properties of an object depend on both geometry and material, which is why we evaluate objects made from plastic and metals. Automatic optimization of natural frequencies can aid in the design of uniquely shaped idiophones, such as bells and xylophones.