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

Area of Science:

• Physics
• Mechanical Engineering
• Materials Science

Background:

• Fabry-Perot resonators (FPRs) are crucial for sensitive optical and microwave measurements.
• Existing structural health monitoring (SHM) uses beams/plates but lacks an explicit FPR framework.
• The dispersive nature of mechanical waveguides poses challenges for FPR application.

Purpose of the Study:

• To establish a theoretical framework for treating flexural beams as FPRs.
• To demonstrate that flexural beam resonances are analogous to Fabry-Perot interference.
• To enable FPR-based sensors for SHM in mechanical waveguides.

Main Methods:

• Analytical derivation of flexural beam behavior as FPRs.
• Wave-propagation analysis to understand resonance mechanisms.
• Fringe-based group-velocity extraction for spectral analysis.

Main Results:

• Flexural beams can be rigorously modeled as FPRs, accounting for dispersion.
• Resonances in beams arise from multi-reflection interference, similar to FPRs.
• A closed-form relationship between group velocity and FPR free spectral range (FSR) was derived.

Conclusions:

• The study provides a theoretical foundation for dispersive mechanical waveguide-based FPR sensors.
• This framework allows for inverse determination of mechanical/environmental changes from fringe spectra.
• Enables advanced SHM applications using FPR principles in mechanical systems.