Analytical expressions of intrinsic internal friction based on damping data under inhomogeneous strains

Abstract

The effect of a strain distribution in a vibrating specimen on the amplitude-dependent damping is analysed for several kinds of measurements. An analytical procedure is given for converting damping data measured as a function of the maximum strain amplitude under inhomogeneous strains to intrinsic internal friction expressed as a function of the homogeneous strain amplitude. On the basis of the analysis by Povolo and Gibala, correct mathematical expressions of internal friction are derived for longitudinal, flexural and torsional modes of free resonant vibrations. The formulae obtained are applied to an experimental curve of damping which increases according to a power of the maximum strain amplitude.