A simplified modal analysis based on the properties of the transfer matrix

The present work describes a range of theoretical and experimental studies on the binary and ternary solid elastic systems, with the aim of outlining a method for determination of elastic constants of certain materials such as small samples that do not allow individual resonance measurements. Although in some particular cases, the spatial arrangement seems to be similar to the Hopkinson split bar experiment, there are major differences because while the Hopkinson split bar experiment deals with measurements at higher stress levels and is similar to measurements in acoustic tubes, our approach is based on a modal analysis of an embedded elastic system. The idea of this work stems from the properties of the intrinsic transfer matrix, which correlates its real eigenvalues with the eigenmode frequencies of the elastic system. An experimental modal analysis combined with a numerical method permits the estimation of phase velocities and the corresponding elastic constants.

► The work presents an experimental modal analysis combined with a numerical approach. ► Estimation of the phase velocity is based on the properties of the transfer matrix. ► Method can be extended by considering also the attenuation.