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Shear wave modes in an equilateral triangular prismatic bar.

Omar Asfar1, Bruno Morvan2

  • 1Department of Electrical Engineering, Jordan University of Science and Technology, Irbid 22110, Jordan.

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|August 15, 2023
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Summary
This summary is machine-generated.

This study analyzes shear wave propagation in equilateral triangular solid bars, identifying horizontally polarized (SH) and vertically polarized (SV) shear waves. Analytical and numerical methods confirm cutoff wavenumbers and mode shapes for these elastic waves.

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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.