Waves in nonlocal elastic material with double porosity

Linear theory of nonlocal elastic material with double porosity structure is developed within the context of Eringen’s theory of nonlocal elasticity. Energy density function is constructed from the basic variables, and then, constitutive relations are derived, which are used to develop the field equations for an isotropic homogeneous nonlocal elastic material with double porosity. It is found that there may exist four basic plane waves in an unbounded medium consisting of three sets of coupled dilatational waves and an independent transverse wave. The major impact of the presence of nonlocality in the medium is that all the four propagating plane waves face cut-off frequencies. The coupled dilatational waves are dispersive and attenuating in nature, while the transverse wave is dispersive and non-attenuating in nature below their respective cut-off frequencies and beyond which they disappear. It is also noticed that coupled waves are affected by the presence of voids, while the transverse wave is independent of the presence of voids in the medium. In the case of non-Voigt model, the coupled dilatational waves face critical frequencies in the low-frequency range. The effect of nonlocality and voids is shown graphically on the dispersion curve of the plane waves for a particular model.