The equation of state of a microinhomogeneous medium and the frequency dependence of its elastic nonlinearity

High-accuracy acoustic detection of nonclassical component of material nonlinearity

“…In this case, the spatial distribution of nodes and anti-nodes is not sufficient to explain the observed increase of a f and a Q with resonant frequency. Actually, besides producing additional amplitude-dependent dissipation, the effective viscoelastic properties of the defects can lead to a very pronounced frequency-dependent variation of the material nonlinearity (Zaitsev et al, 2001;Zaitsev et al, 2002;Zaitsev and Matveev, 2006). These corrections are different for different materials, and in the case of pastel chalk, the strong discrepancy between the nonlinearity observed for different modes may arise from such a nonhysteretic mechanism competing with the genuine intrinsic hysteretic behavior.…”

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“…Without specifying the types of imperfections, the features noted above can be described by a rather simple rheological model of a microinhomogeneous medium with soft contrasting imperfections [15,16]. Even a one-dimensional variant of the model allows drawing some nontrivial conclusions.…”

“…The parameter g here characterizes the imperfection nonlinearity on the scale of its own deformation e 1 , the magnitude of g being in the standard range of several units. Using this model of a microinhomogeneous medium, for a low concentration of identical defects, we obtain [16] the following relation between the macroscopic material strain and stress:…”

“…The lack of space does not allow us to discuss these and other interesting consequences of the rheological model in more detail [15,16]. We note that its implications are supported by the direct analysis of nonlinear and thermoelastic effects at Hertzian microcontacts in cracks [11,12].…”

Nonlinear multiple scattering of acoustic waves by a layer of bubbles

“…Gas bubbles appear as perfect candidates for looking at nonlinear acoustic propagation in a multiple scattering regime: they are efficient acoustic scatterers, as well as strong nonlinear sources. Bubbly liquids have already been shown to exhibit substantial acoustic nonlinearities [9][10][11][12]. But an important limitation of the previous studies was the lack of quantitative comparison between the theoretical predictions and the experimental measurements, often due to a weak knowledge of the structure of the bubbly liquids used for the experiments.…”