Measuring of Cosserat Effects and Reconstruction of Moduli Using Dispersive Waves
We revisit the problem of identification of effects of independent rotations and reconstruction of the parameters of Cosserat continuum. The effect of rotational degrees of freedom leads to the appearance of additional shear and rotational waves; however, only at high frequencies corresponding to the wave lengths comparable to the microstructural sizes. Such waves are difficult to detect. Rotations also affect the conventional s-waves (shear-rotational waves) making them dispersive for all frequencies. We considered propagation of planar waves in 2D granulate materials consisting of parallel cylindrical particles connected by tensile, shear and rotational springs and arranged in either square or hexagonal patterns. We deduced the s-wave dispersion relationships for both cases and determined the main terms of asymptotics of low frequency; they were found to be quadratic in the frequency. These terms, alongside with the zero order terms, can be determined by fitting of the theoretically determined frequency dependence of the phase shift between the sent and received wave to its experimentally determined counterpart. This opens a way for direct experimental identification of Cosserat effects in granulate materials.
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