Analytical solutions for sagittal plane waves in three-layer composites

Area of Science:

• Acoustics
• Materials Science
• Solid Mechanics

Background:

• Plate wave sensors are vital for detecting mass loading and chemical changes.
• Understanding wave propagation in layered composites is key to sensor design.
• Acoustically thin layers (<0.02 lambda) present unique challenges and opportunities in sensor applications.

Purpose of the Study:

• To derive analytic dispersion equations for symmetric and antisymmetric sagittal plane plate modes in a three-layer composite.
• To determine the influence of elasticity and inertia of thin layers on phase velocity and mass loading sensitivity.
• To analyze the frequency dependence of sensor sensitivity for the lowest symmetric (S(0)) and antisymmetric (A(0)) modes.

Main Methods:

• Derivation of analytic dispersion equations for a three-layer composite system.
• Analysis of thin layers as mass loading or chemical selective coatings.
• Formulation of explicit equations for phase velocity and mass loading sensitivity.
• Investigation of elasticity and inertia effects on sensor performance.

Main Results:

• Explicit formulas were obtained for the phase velocity and mass loading sensitivity of S(0) and A(0) modes in thin composite plates.
• The study quantifies how thin layer elasticity and inertia reduce mass loading sensitivity.
• The sensitivity of the A(0) mode was found to be frequency-dependent, unlike the S(0) mode.

Conclusions:

• The derived equations provide a theoretical basis for designing and optimizing plate wave sensors.
• The findings highlight the distinct frequency-dependent behavior of S(0) and A(0) modes, enabling tailored sensor applications.
• The study offers insights into the trade-offs between sensor sensitivity and the physical properties of composite layers.