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Topology and Shape Optimization Under Uncertainty for Multifunctional Metamaterials 

Recently, it was demonstrated that the integration of mechanical resonators based on piezoelectric materials inside a periodic structure enables capabilities that can be used for vibration suppression and energy harvesting. This configuration is promising since it can be helpful in civil and mechanical applications, for example, in designing non-structural walls and machine enclosures/supports with dual capabilities: acoustic/vibration isolation and energy harvesting. However, studying and understanding these dual-purpose piezoelectric-based metamaterials is an emerging research field, and many questions remain open, particularly considering optimization under model parameter uncertainty. The overall goal is to develop a framework for shape and topology optimization under parametric uncertainties for metamaterials composed of periodic arrays of piezoelectric-based resonators for both wave filtering and energy harvesting. This modeling approach can be readily extended to metamaterials with different functionalities, for example, to generate photonic bandgaps or negative refractive index materials. 

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