![]() ![]() Generally, the first kind of compressional wave, which is known as Biot’s wave of the first kind or the first wave, is a weakly decaying high-velocity mode, while the second kind of compressional wave, which is known as Biot’s wave of the second kind or the second wave, is a strongly damping slow-velocity mode. The wave mode, dispersion relation, and transfer function are proposed. ![]() Īs is well known, the first and second kind of compressional waves exist in saturated porous media, which are predicted by the Biot theory. Solutions are obtained by a perturbation technique in closed-form for normal, shear stresses, dielectric displacement, and electric potential, and it is found that the complex phase velocity with positive imaginary part increases with time. Initial and couple stress influence on transmission of the Love-type wave, and Rayleigh waves in material layers with imperfect interface, and surface wave propagation between viscous liquid and initially stressed piezoelectric half-space are investigated by using the spatial varying WKB (Wentzel-Kramers-Brillouin) method. Different investigations are available in literature focusing on the mechanical behaviors of piezoelectric nanostructures on fields of linear and nonlinear, longitudinal and transverse, free and forced wave propagation in microscale. Compressional waves in saturated porous media have found geophysical interests to hydraulic fracturing, oil exploration, volcanic eruptions, and magneto-electro-elastic behavior of piezoelectric nanostructures. Propagation of acoustic waves through saturated porous media is a phenomenon of great fundamental importance and increasing technological relevance, which is significant to obtain better surface acoustic wave device’s performance. The introduction of the Darcy-Brinkman law yields an improved description of the damping of the compressional wave modes in saturated porous media. A key finding is that, compared to the Darcy-Brinkman law, Darcy’s law overestimates the phase velocity, damping, and phase lag of the first wave, while underestimates the phase velocity, damping, and phase difference of the second wave. The coincidence of the properties of Biot waves of the first and second kinds occurs at a characteristic frequency, which is remarkably influenced by the Brinkman term. The Brinkman term describes the fluid viscous shear effects and importantly contributes to the dispersion relation and wave damping. The wave mode, phase velocity, phase lag, damping factor, and characteristic frequency are found from the updated mathematic model. Propagation of pore pressure and stress in water-saturated elastic porous media is theoretically investigated when considering the Darcy-Brinkman law. ![]()
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