High-Frequency Low-Loss Ultrasonic Modes in Imbedded Bars

The dispersion relationships of a system comprising a circular bar imbedded in a solid medium having a lower acoustic impedance than the bar have been predicted. A generic study of such systems has been undertaken, motivated by a particular interest in the case of a circular steel bar imbedded in cement grout which has application to the inspection of tendons in post-tensioned concrete bridges; measurements to confirm the predictions have been carried out for this case. The attenuation dispersion curves show a series of attenuation minima at roughly equal frequency spacing. The attenuation minima occur at the same frequencies as energy velocity maxima and they correspond to points at which the particle displacements and energy of the particular mode are concentrated towards the center of the bar so leakage of energy into the imbedding medium is minimized. The attenuation at the minima decreases with increasing frequency as the energy becomes more concentrated at the middle of the bar, until the material attenuation in the bar becomes a significant factor and the attenuation at the minima rises again. For the particular case of a steel bar in cement grout, the minimum attenuation is reached at a frequency-radius product of about 23 MHz-mm. The frequency-radius product at which the minimum attenuation is reached and the value of the minimum attenuation both increase as the acoustic impedance of the imbedding medium increases.