Predictive Model for the Dissipation Dilution of Soft-Clamped Modes in Polygon Resonators
Polygon resonators are promising candidates for nanomechanical applications due to their compact architecture and high force sensitivity. Here, we develop a polygon-specific analytical model for perimeter modes by coupling the flexural motion of the polygon sides to tether torsion governed by a stress-modified Timoshenko-Gere (TG) equation. The model captures finite-wavelength torsional phase accumulation beyond the conventional short-tether approximation, revealing tether-length-dependent resonances and bending-torsion hybridization. Comparisons with finite-element-method (FEM) simulations show good agreement in the quasi-one-dimensional regime, while identifying the onset of deviations associated with neglected torsional deformation of the polygon sides. The model therefore provides a useful analytical tool for interpreting and optimizing high quality factor (Q) polygon resonators for cavity optomechanics and precision sensing.