Metamaterials are compound structures that are made from small sub structures called unit cells. This compound structure allows them to have customizable physical properties, without the need to use more expensive material or increased system mass. Therefore they are popularly used in different applications such as acoustics, photonics, and sensing. Aperiodic meta materials are essentially structural systems that are composed on different types of cells, instead of repetitions of the same unit cell topology. Optimizing aperiodic cellular structural systems thus presents high-dimensional design problems, that become intractable to solve using purely high-fidelity structural analysis coupled with optimization. Specialized analytical modeling along with metamodel based optimization can provide a more tractable alternative to designing such aperiodic metamaterial systems. To explore this concept, this paper presents an initial design automation framework, applied on a case study representative of a 1D metamaterial system. The case in consideration is a drill string, where vibration suppression is of utmost importance. This is achieved by using nonuniform rings imposed on the drill string, where the drill string can now be perceived as a aperiodic 1D metametaral system with each ring/gap represent a cell. While being a 1D system, the simultaneous consideration of multiple degrees of freedom (related to torsional, axial and lateral motions) poses significant computational challenges. To deal with these challenges, a transfer matrix method (TMM) is used to analytically determine the frequency response of the drill string. However, due to minute scale cost of the TMM method, the optimization remains computationally burden-some. This later challenge is addressed by training a suite of neural networks on a set of TMM samples, with each network providing the response w.r.t. a specific frequency. Optimization is then performed to minimize mass subject to constraints on the gap between consecutive resonance peaks in one case, and minimize this gap in the second case. Crucial improvements are accomplished over the initial baselines in both cases. An inverse model is also developed and preliminarily evaluated with aim of directly yielding the drill string ring geometry/distribution w.r.t. specified frequency response.


Metamodel Based Forward and Inverse Design for Passive Vibration Suppression

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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