Ultrasonic elastic modes in solid bars: an application of the plane wave expansion method.

Ultrasonic elastic modes in solid bars are investigated theoretically and experimentally using the plane wave expansion method to calculate the dispersion curves k=k(omega) for longitudinal, torsional, and flexural waves. The plane wave extension method allows to consider rods of circular and square cross sections. The technique, which has received attention in the study of photonic and phononic crystals, is adapted in order to identify the various types of modes. Results are compared with predictions from semi-analytical models. The numerical approximation is validated with the experimental determination of the time-frequency dispersion curves. The technique based on the plane wave expansion method presented here could be a numerical alternative used to determine the wave propagation and modal vibration with high precision in structures like bars and cylinders. Practical applications of this study could include the inspection of long-span engineering systems with bar or cylinder like characteristics.