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Materials 2017, 10(10), 1125; doi:10.3390/ma10101125

Design and Additive Manufacturing of 3D Phononic Band Gap Structures Based on Gradient Based Optimization

1
Joint Institute of Advanced Materials and Processes (ZMP), Friedrich-Alexander-University Erlangen-Nürnberg, 90762 Fürth, Germany
2
Department Mathematik, Mathematical Optimization, Friedrich-Alexander-University Erlangen-Nürnberg, 90762 Fürth, Germany
3
Materials Science and Technology for Metals (WTM), Friedrich-Alexander-University Erlangen-Nürnberg, 90762 Fürth, Germany
*
Author to whom correspondence should be addressed.
Received: 7 August 2017 / Revised: 14 September 2017 / Accepted: 15 September 2017 / Published: 22 September 2017
(This article belongs to the Special Issue Auxetic Materials 2017)
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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. View Full-Text
Keywords: phononic band gap; additive manufacturing; selective electron beam melting; cellular materials; metamaterials; topology optimization; parametric shape optimization; gradient based optimization phononic band gap; additive manufacturing; selective electron beam melting; cellular materials; metamaterials; topology optimization; parametric shape optimization; gradient based optimization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wormser, M.; Wein, F.; Stingl, M.; Körner, C. Design and Additive Manufacturing of 3D Phononic Band Gap Structures Based on Gradient Based Optimization. Materials 2017, 10, 1125.

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