Determination of dynamic elastic properties from the frequency of natural vibration by using impact acoustics

摘要

The dynamic elastic properties of rocks can be determined in a non-destructive manner by using dynamic resonance methods. As mentioned in the industrial standards like JIS A 1127 or ASTM E 1876, the dynamic elastic properties of a material can be computed if the geometry, mass, and mechanical resonant frequencies of a suitable (rectangular or cylindrical geometry) test specimen of that material can be measured. The dynamic Young's modulus is determined using the resonant frequency in either the flexural or longitudinal mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. In this study, prismatic columnar specimen is used to investigate the elastic properties of various types of rocks by measuring the frequencies of natural vibration. The measuring system consists of an impact acoustic generator and a receiver. The impulse tool is used to provide a single elastic strike to the test specimens to induce the fundamental resonant frequency and the receiver senses the resulting mechanical vibrations. Specimen supports, impulse location, and signal pick-up points are selected to induce specific modes of the transient vibrations. The results obtained by the above-mentioned systems are compared with those obtained by the ultrasonic methods with significantly acceptable coincidence between the two methods. Then, some basic experiments are carried out to clarify the influences of defects on the amplitude and resonant frequency of impact acoustics. Even though it is difficult to evaluate the equivalent elastic properties of a cracked specimen by ultrasonic methods, the simple impact acoustic methods are applicable. Numerical analyses are conducted to determine the relationships between the natural frequency and elastic properties.