Gage-length errors in the resolution of dispersive stress waves

The effect of measuring the time history of a passing dispersive wave with a finite-length gage is to introduce time and amplitude errors between the actual values and the measured values of the wave function. In this paper, mathematical expressions relating the size of these errors to the gage length, properties of the material, and spectral content of the incident wave are derived. These expressions are used to predict the response of a long, resistance strain gage, attached in the longitudinal direction on the lateral surface of a long slender rod of a linear viscoelastic material (Lexan), to a short pulse. The shape of the pulse just before and just after the region of the long gage was measured by means of very short gages. The dispersion and attenuation properties of the material were obtained from the short-gage data. This information and the previously derived mathematical-correction equations were used to predict the response of the long gage. Good agreement was obtained between the predicted and measured values of the response of the long gage. In addition, the correction equations and the response of the long gage were used to predict the incident pulse. Good agreement with the known experimental values was obtained.