Fixed-phase Resonance Tracking for Fast Nonlinear Resonant Ultrasound Spectroscopy
Nonlinear Resonant Ultrasound Spectroscopy (NRUS) experiments that rely on repeated sampling of resonance curves are inherently sensitive to measurement protocol due to evolution of material parameters caused by fast and slow dynamic effects. We introduce a model-assisted discrete-time resonance tracking method that maintains a system at its instantaneous resonance condition without the need to acquire full frequency sweeps. Resonance is defined through a prescribed phase relation between excitation and response, and the excitation frequency is iteratively updated using a linearized frequency--phase model. The procedure allows controlled suppression of transient wave buildup using optional feedforward correction with respect to an external control parameter. The method is demonstrated on NRUS and performing a conditioning-relaxation protocol, both conducted on a sandstone bar, providing estimates of resonance frequency and damping. Comparison with conventional approaches shows that measurement speed and mode stability significantly influence the inferred nonlinear indicators. The proposed framework is not limited to nonlinear acoustics and can be applied to arbitrary resonant systems with slowly evolving parameters.