Empirical identification of a robust spectral knee in multiharmonic cantilever measurements

Harmonic amplitudes in microcantilever oscillators carry critical information for nanoscale force and material characterization, yet their decay behavior across different environments remains insufficiently quantified. Here, we characterize multiharmonic cantilever spectra in air and liquid under tapping and free-vibration conditions, revealing a consistent two-regime power-law decay separated by a knee at mode index n^⋆ that shifts systematically with environment. Employing robust segmented regression, bootstrap confidence intervals, and modal lifetime overlap analysis, we identify the knee as a stable spectral feature linked to transitions in viscous confinement and near-surface interphase memory. This framework enables compact parametrization of harmonic spectra and may provide a practical route to distinguish medium-dominated dissipation from interfacial viscoelastic effects. Our findings advance the understanding of cantilever-fluid-interphase dynamics and suggest new avenues for quantitative multiharmonic nanomechanical metrology.