Complete mode identification for resonance ultrasound spectroscopy

Abstract

This study is devoted to deducing exact elastic constants of an anisotropic solid material without using any advance information on the elastic constants by incorporating a displacement-distribution measurement into resonant ultrasound spectroscopy (RUS). The usual RUS method measures free-vibration resonance frequencies of a solid and compares them with calculations to find the most suitable set of elastic constants by an inverse calculation. This comparison requires mode identification for the measured resonance frequencies, which has been difficult and never been free from ambiguity. This study then adopts a laser-Doppler interferometer to measure the displacement-distribution patterns on a surface of the vibrating specimen mounted on pinducers; comparison of the measured displacement distributions with those computed permits us to correctly identify the measured resonance frequencies, leading to unmistakable determination of elastic constants. Because the displacement patterns are hardly affected by the elastic constants, an exact answer is surely obtained even when unreasonable elastic constants are used as initial guesses at the beginning of the inverse calculation. The usefulness of the present technique is demonstrated with an aluminum alloy and a langasite crystal.

In situ laser-based resonant ultrasound measurements of microstructure mediated mechanical property evolution

“…One indication that a single mode is tracked is that the mode location is a smooth function of temperature. In addition, because the mode shapes are relatively insensitive to changes in the elastic properties that occur during annealing, 35 the mode shapes before and after annealing can be used to further support that a single mode was tracked throughout the entire cycle. The in situ mode position for a single mode is shown in Fig.…”

Resonant ultrasound spectroscopy for investigation of thin surface coatings

“…For homogeneous, bulk specimens of simple geometry, this can be easily achieved by finding stationary points of the Lagrangian energy of the vibrating specimen (a simple variational problem, which can be easily solved by Ritz method, see e.g. [5,7,10,12]). In the following section, the direct problem will be posted and solved for a substratecoating system.…”

“…where α is a vector of coefficients from approximation (2) and the matrices K and M are given by the geometry, density and elastic coefficients of the substrate [5,7,10,12].…”

“…The measurements were further improved by scanning the surface of the resonating specimen by a laser vibrometer, thus not only the resonant frequencies but also the shapes of vibration modes became available. In 2002, Ogi et al [7] used this improvement for reliable identification of individual modes in the obtained spectrum, which was the approach further developed by the authors in the past few years [8][9][10][11][12].…”

“…The main improvement brought by the Ogi's group to the experimental embodiment of RUS lies in a novel experimental scheme, so-called tripod scheme (e.g. [7]). In this scheme, the investigated specimen is freely laid in a tripod of thin, rod-like piezoelectric transducers (one of them is used for generation of vibrations, the others for detection of the specimen's response).…”