Recent advancements in nanofabrication have enabled the creation of nanomechanical resonators (NMRs) with extreme aspect ratios, paving the way for high-performance resonators that can couple to light, quantum systems or other matters. A key requirement for such applications is achieving an exceptionally high mechanical quality factor, Q, which indicates minimal energy dissipation and strong isolation from environmental noise. Among various structural approaches, periodic phononic crystal (PnC)-based membrane resonators have demonstrated high Q values (10e8) with outstanding practicality, but their performance is fundamentally limited by the constraints of two-dimensional periodicity.

This thesis proposes an alternative design strategy based on 2D quasicrystal (QC) geometries, which are aperiodic yet possess rotational symmetries in certain variants. QC-based designs offer greater flexibility and potentially richer dynamics compared to conventional periodic PnCs. However, their geometric complexity and lack of established theoretical frameworks require advanced, computation-heavy design and optimization techniques. To address this, we introduce a data-driven design and optimization framework tailored for QC-based resonator designs. Our results demonstrate the promising potential of moving beyond periodic structures to aperiodic designs in the pursuit of ultra-high Q nanomechanical resonators.