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Longitudinal waves at a micropolar fluid/solid interface. (English) Zbl 1167.74462

Summary: The possibility of plane wave propagation in a micropolar fluid of infinite extent has been explored. The reflection and transmission of longitudinal elastic wave at a plane interface between a homogeneous micropolar fluid half-space and a micropolar solid half-space has also been investigated. It is found that there can exist four plane waves propagating with distinct phase speeds in an infinite micropolar fluid. All the four waves are found to be dispersive and attenuated. The reflection and transmission coefficients are found to be the functions of the angle of incidence, the elastic properties of the half-spaces and the frequency of the incident wave. The expressions of energy ratios have also been obtained in explicit form. Frequency equation for the Stoneley wave at micropolar solid/fluid interface has also been derived in the form of sixth-order determinantal expression, which is found in full agreement with the corresponding result of inviscid liquid/elastic solid interface. Numerical computations have been performed for a specific model. The dispersion curves and attenuation of the existed waves in micropolar fluid have been computed and depicted graphically. The variations of various amplitudes and energy ratios are also shown against the angle of incidence. Results of some earlier workers have been deduced from the present formulation.

MSC:

74J15 Surface waves in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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