Direct and inverse problems of linear resonant ultrasound spectroscopy

Abstract

The model approach of linear resonance ultrasound spectroscopy (LRUS) is described: obtaining the elastic moduli and Q values from resonance spectral measurements at frequencies ranging from several kHz to tens of kHz on complex solids such as rock. In the direct (forward) problem, LRUS is based on the variational principle, that of determining the eigenvalues from resonance spectral peaks of samples (complex in the general case). By minimizing the difference between the measured and calculated resonant modes for a given geometry of the sample, the linear properties of the sample (inverse problem) can be determined. The method was tested by comparing theoretical and experimental results obtained by Demarest [H. Demarest, J. Acoust. Soc. Am. 49, 768–775 (1971)] and data obtained from experiments carried out in IAP RAS on rectangular bricks at audio frequencies. Comparison of measured and calculated data showed that the difference may be as low as 0.6%. [This work is supported by the United States Industry Coalition, with the U.S. DOE, Contract No. W-7405-ENG-36, through the University of California.]