Full-spectrum-based acoustic spectroscopy for determining elastic and damping constants in forced-free bars

Abstract

Elastic moduli and damping have been previously determined by measuring the resonant frequencies and quality factor of a virtually free–free bar. The development of a complete analytical solution to the longitudinal wave equation including damping effects for a bar freely supported, driven at one end, and under the influence of transducer mass and stiffness at both ends was previously reported on [Qiushuang Guo and David Brown, ‘‘Effects of transducer mass on resonance frequency and quality factor of free-free bar,’’ J. Acoust. Soc. Am. 101, 3062 (1997)]. The analytical solution to the torsional and flexural waves in a bar including damping effects will be reported on here. When the entire spectrum of data is used, a more accurate determination of elastic moduli and internal damping coefficient is obtained. [Work supported by the University of Massachusetts—Dartmouth.]