Nature's Microfabricated 3D Coupled Dual-Membrane Resonators-A Dynamic Analysis of Circular Diatom Frustules

MEMS (microelectromechanical system) resonators, meticulously fabricated by advanced lithographic and etching processes, have become indispensable technological cornerstones across modern sensing, time-keeping and actuation applications. Yet, realising 3D coupled architectures for these silicon-based resonators remains a fundamental microfabrication challenge, limiting the toolkit of exploitable dynamic phenomena to the in-plane and flexural modes. Nature, however, through 200 million years of evolutionary refinement, has nano-engineered a ready-made solution: the diatom frustule made from biosilica (SiO₂), a robust material with mechanical properties well-suited to micro-mechanical resonator applications. Unlike planar MEMS counterparts, frustules are typically dual-membrane structures, vertically coupled by a girdle band, introducing complex 3D coupling dynamics that are prohibitively complex to achieve with MEMS fabrication. This paper explores the analytical and numerical modelling of a typical circular frustule's dynamic behaviour. Alongside the typical transverse modes expected from MEMS resonators, the 3D coupled structure also exhibits unique girdle band tilt modes, exclusively activated by antisymmetric excitations. Collectively, the presence of partial mode localisation, mechanical energy amplification through the low-inertia girdle band, and rotational-transverse modal coupling, demonstrates the diatom frustule to be a dynamically rich resonator. This establishes the theoretical framework for exploiting the diatom frustule as a novel bio-inspired and bio-derived 3D resonator building block.