Shear wave modes in an equilateral triangular prismatic bar

Area of Science:

• Solid mechanics
• Acoustics
• Wave propagation

Background:

• Understanding wave propagation in non-circular geometries is crucial for material characterization.
• Previous studies have explored wave phenomena in simple geometries, but complex cross-sections like triangles require detailed analysis.

Purpose of the Study:

• To investigate the existence and characteristics of horizontally polarized (SH) and vertically polarized (SV) shear waves in equilateral triangular solid bars.
• To determine the cutoff wavenumbers and analyze the mode shapes of these shear waves.
• To validate analytical solutions with numerical simulations and experimental data.

Main Methods:

• Analytical solutions based on Lamé's theory for SH waves and symmetrical component analysis for SV waves.
• Numerical simulations using COMSOL to calculate dispersion curves and cutoff wavenumbers.
• Experimental verification using laser vibrometer to measure normal displacement mode shapes.

Main Results:

• Identified SH wave modes as Lamé solutions derived from plane wave superposition and reflections.
• Determined cutoff wavenumbers for Neumann SH modes (4mπ/(3a)) and the first Dirichlet SH mode (4π7/(3a)).
• Related SV modes to sub-triangles, with cutoff wavenumbers between the first and second Neumann SH modes.
• Confirmed analytical predictions with COMSOL simulations and experimental measurements.

Conclusions:

• The study successfully elucidates the behavior of SH and SV shear waves in equilateral triangular bars.
• Analytical models provide accurate predictions for wave characteristics, validated by numerical and experimental data.
• This research contributes to the understanding of wave dynamics in complex solid geometries.