Abstract
We present a novel approach for gradient based maximization of phononic band gaps. The approach is a geometry projection method combining parametric shape optimization with density based topology optimization. By this approach, we obtain, in a two dimension setting, cellular structures exhibiting relative and normalized band gaps of more than 8 and 1.6, respectively. The controlling parameter is the minimal strut size, which also corresponds with the obtained stiffness of the structure. The resulting design principle is manually interpreted into a three dimensional structure from which cellular metal samples are fabricated by selective electron beam melting. Frequency response diagrams experimentally verify the numerically determined phononic band gaps of the structures. The resulting structures have band gaps down to the audible frequency range, qualifying the structures for an application in noise isolation.
Highlights
In the last 25 years since their emergence, materials with phononic band gap (PBG) are gaining more interest among scientists
We present novel PBG structures obtained by our new optimization approach
We developed a parametric shape optimization approach which allows us to explicitly formulate the connectivity requirement as given, with no design freedom at hand for the optimizer to remove the connectivity for the sake of PBG maximization
Summary
In the last 25 years since their emergence, materials with phononic band gap (PBG) are gaining more interest among scientists. A PBG describes a frequency band where mechanical waves are not transmitted through a material. For applying the concept of PBGs in real life, the need for design methods to precisely predict the resulting PBG frequency range arises. Phononic crystals, named based on the previously discovered photonic crystals, are periodic binary composites and were the first structures identified to have a PBG [1]. These composites consist of periodic inclusions that act as scatterers and a matrix with a large mismatch in elastic constants compared to the inclusions [2]. While the first numerical proof of this concept goes back to 1993 [3], the first experimentally observed PBG in a phononic crystal was documented in 1995 and a complete PBG was first documented in 1998 [4,5]
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