Regulation of Three Different Nonlinear States in Micromechanical Resonators

The introduction of nonlinearity has broadened the performance and application range of micro-mechanical resonators, making the design and regulation of tailored nonlinear properties crucial—necessitating the identification of distinct nonlinear states. While traditional models account for either hardening or softening nonlinearities, they often overlook mixed nonlinearity, which manifests as dual jumps—right-sided (hardening) and left-sided (softening)—in the amplitude-frequency response. To clarify the transitions among hardening, softening, and mixed states, we performed experiments on a single micro-mechanical straight beam, where all three regimes were induced by modulating the excitation and electrothermal current. Based on the observed backbone curves, we developed an analytical model to characterize the boundaries of these nonlinear states. The model shows good agreement with experimental observations, supporting its effectiveness in capturing the underlying trends. Rather than providing exact predictions, the model offers insights into how the quadratic and cubic nonlinear coefficients, along with excitation intensity, influence state transitions. These findings contribute to a better understanding of nonlinear behavior and offer guidance for the design and regulation of nonlinear states in micro-mechanical systems.[2025-0044].