Nonlinear Mode Coupling in Silicon Nitride Membrane Resonators

Abstract: Nonlinear interactions between vibrational modes play a crucial role in understanding the dynamical response of nanomechanical resonators. Here, we report the experimental observation and theoretical modeling of nonlinear mode coupling in a high-stress square silicon nitride membrane resonator. We quantify frequency shifts of the fundamental mode arising from tension-mediated geometric nonlinearity by increasing the amplitude of the fundamental mode and higher-order flexural modes. A quantitative theoretical framework based on Kirchhoff-Love plate theory is developed, which incorporates both intrinsic Duffing nonlinearity and nonlinear intermodal coupling and shows good agreement with experimental measurements for the (1,1)-(2,1) and (1,1)-(2,2) mode pairs. We further compute the nonlinear coupling matrix across mode families, revealing the role of mode symmetry and spatial overlap in governing intermodal interactions. These results establish nonlinear mode coupling as a controllable resource for multimode frequency tuning and mechanical transduction.