  Optimization of functionally graded metamaterial arrays with a high
dimensional and continuous geometric design space is cumbersome and could be
accelerated via machine learning tools. Mechanical metamaterials can manipulate
acoustic or ultrasonic waves by introducing large dispersive and attenuative
effects near their natural frequency. In this work functionally graded
structures are designed and optimized to combine the energy attenuation
performance of a number of unit cells with varying frequency responses and to
reduce the interlayer mismatch effects. Optimization through genetic algorithm
avoids the many local minima related to high dimensionality of the design space
but requires many iterations. A reduced order model (ROM) is applied that can
reproduce the transmission response that is traditionally calculated with FEM,
in a fraction of the time. Pairing GA and the ROM together, an array of 6 unit
cells (with a total of 18 independent geometric design variables) is optimized
to have stop bands with extended width and sharper boundaries. Symmetric
functionally graded structures are determined to be optimal geometric
configurations. Measured 3D printed features are projected onto the ROM
solutions to quantify the effect of printing uncertainty on array performance.
Repeatability error of $\pm~20$ $\mu$m is determined to reduce the mean depth
of the transmission stop band by a factor of $10^2$ and introduce small shifts
in center frequency and band width. Proposed methods to improve the resolution
of accessible points in the ROM space, reduce sensitivity to geometric
uncertainty, and add design freedom include introducing out-of-plane
perforations and varying constituent materials using tunable filled resin
systems.

Applied Physics