  Aperiodic metamaterials represent a class of structural systems that are
composed of different building blocks (cells), instead of a self-repeating
chain of the same unit cells. Optimizing aperiodic cellular structural systems
thus presents high-dimensional problems that are challenging to solve using
purely high-fidelity structural optimization approaches. Specialized analytical
modeling along with metamodel based optimization can provide a more tractable
alternative solution approach. To this end, this paper presents a design
automation framework applied to a 1D metamaterial system, namely a drill
string, where vibration suppression is of utmost importance. The drill string
comprises a set of nonuniform rings attached to the outer surface of a
longitudinal rod. As such, the resultant system can now be perceived as an
aperiodic 1D metamaterial with each ring/gap representing a cell. Despite being
a 1D system, the simultaneous consideration of multiple DoF (i.e., torsional,
axial, and lateral motions) poses significant computational challenges.
Therefore, a transfer matrix method (TMM) is employed to analytically determine
the frequency response of the drill string. A suite of neural networks (ANN) is
trained on TMM samples (which present minute-scale computing costs per
evaluation), to model the frequency response. ANN-based optimization is then
performed to minimize mass subject to constraints on the gap between
consecutive resonance peaks in one case, and minimizing this gap in the second
case, leading to crucial improvements over baselines. Further novel
contribution occurs through the development of an inverse modeling approach
that can instantaneously produce the 1D metamaterial design with minimum mass
for a given desired non-resonant frequency range. This is accomplished by using
invertible neural networks, and results show promising alignment with forward
solutions.
