Flexural Beams as Mechanical Fabry-Perot Resonators: A Theoretical Framework for Dispersive Waveguide-Based Sensing.

Fabry-Perot resonator (FPR) sensors are widely implemented in optical and microwave waveguides because their interference fringe spectra enable highly sensitive, stable, and calibration-free measurements. In contrast, despite the extensive use of beams and plates as waveguides in vibration- and ultrasound-based structural health monitoring (SHM), an explicit FPR framework for these mechanical waveguides has not been established. This paper demonstrates that flexural beams can be rigorously treated as FPRs despite their inherently dispersive nature. Through analytical derivation, wave-propagation analysis, and fringe-based group-velocity extraction, we show that flexural-beam resonances arise from multi-reflection interference analogous to Fabry-Perot interference. A closed-form relationship between the frequency-dependent group velocity and the FPR free spectral range (FSR) is established, enabling inverse determination of mechanical or environmental perturbance from the FPR fringe spectrum. By extending FPR-based fringe analysis to dispersive mechanical waveguides, this work introduces a theoretical framework for implementing dispersive mechanical waveguide-based FPR sensors.