## 5aPA6. Simultaneous determination of elastic constants and asphericity of aspherical specimen by the resonant sphere technique.

### Session: Friday Morning, May 17

**Author: Hitoshi Oda**

**Location: Dept. of Earth Sciences, Okayama Univ., Okayama, 700 Japan**

**Abstract:**

The resonant sphere technique (RST) is a method of resonant ultrasound
spectroscopy developed to measure elastic constants of solids. In this method,
resonant frequencies of a spherical specimen are measured and the elastic
constants are determined by comparing the measured frequencies with theoretical
ones that have been computed for a set of elastic constants. A perfect sphere is
not always obtained, however; the specimen sometimes has small asphericity. In
this case, the effect of asphericity on the resonant frequencies has to be
corrected. Thus a method has been developed to determine simultaneously the
elastic constants and asphericity of an aspherical specimen. When RST is
employed for elasticity measurements of an ellipsoidal specimen, the difference
between measured and computed resonant frequencies is expressed by
(delta)(omega)=(phi)[inf i](epsilon)[inf i]+A[inf ij](delta)C[inf ij], where
summation convention is assumed for repeated indices, and (epsilon)[inf i] and
(delta)C[inf ij] (i,j=x,y,z) are asphericity of the ellipsoid and small
corrections for a set of elastic constants, respectively. Since the coefficients
(phi)[inf i] and A[inf ij] are known, the unknown coefficients (epsilon)[inf i]
and (delta)C[inf ij] can be determined by a least-squares method. Actual
application will be reported for an ellipsoid of an olivine specimen with
orthorhombic crystal symmetry.

from ASA 131st Meeting, Indianapolis, May 1996