Determination of the dynamic elastic moduli and internal friction using thin resonant bars

Analysis of the data from the resonant-bar technique for determining wave speed and internal friction is presented. Internal friction has been included in the longitudinal and torsional wave equations and the analytical solution has been obtained. In determining the acoustical constants of lossy materials, a broad frequency spectrum is used that includes many resonances and not just data at or near the individual resonances. Corrections due to the mass, length, stiffness, and damping of the transducers are also presented. The theoretical solutions are compared with the measured magnitude and phase response data for torsional, longitudinal, and flexural measurements and are shown to be in good agreement.