Sensitive determination of nonlinear properties of berea sandstone at low strains

Resonant response functions of a sandstone bar, measured at strain magnitudes between 10 −8 and 10 −6 at several temperatures, are used to extract Young's modulus and loss tangent as functions of frequency and driving force. Expressing the distorted shape of nonlinear resonances in terms of shifts in the resonant frequency and Q enables correlation analysis of these functions against components of the strain response function. Resonance shifts are found to be strongly correlated with somewhat complicated functions of strain, but only weakly with frequency or phase of the response. Decomposing the data along contours of constant strain magnitude yields the quantitative scaling of resonance shifts with strain, which shows a superposition of both conventional and necessarily hysteretic nonlinear sources. No statistically significant temperature dependence is found in the coefficients of the fits.