Cascade of Modal Interactions in Nanomechanical Resonators with Soft Clamping

Abstract: Cascades of dynamical phenomena, where energy and motion transfer across coupled degrees of freedom, underlie complex behavior in physical systems spanning multiple time and length scales. Here, we demonstrate that soft-clamping techniques commonly employed to enhance the quality factor of nanomechanical resonators, can also be harnessed to engineer cascaded energy transfer conditions, enabling the sequential excitation of an increasing number of coupled vibrational modes during frequency sweeps. Using Si3N4 nanostrings with soft-clamping supports, we identify the conditions for mode coupling and obtain interactions among five flexural resonances , achieving a quasi-constant amplitude of the targeted resonant response over a broad frequency range. Analytical and nonlinear reduced-order models reveal that soft clamping can not only facilitate a sequence of interactions, but also amplify the geometric nonlinearity of the driven mode, enhancing effective spring hardening by more than an order of magnitude through dispersive couplings. This ability to activate and control energy flow in nanomechanical systems offers a strategy for realizing programmable nonlinear dynamics for next-generation resonators.