Rayleigh Wave in a Micropolar Elastic Medium with Impedance Boundary Conditions

In this paper, a problem on Rayleigh surface wave in an isotropic micropolar elastic solid half-space with impedance boundary conditions is investigated. It is assumed that the normal force traction, shear force traction and shear couple traction vary linearly with the normal displacement component, tangential displacement component and microrotation component multiplied by the frequency, where the impedance corresponds to the constants of proportionality. The linear governing equations of an isotropic micropolar elastic medium are solved for general surface wave solutions. The appropriate particular solutions satisfying the radiation conditions in a half-space of medium are applied at the free surface of the half-space with impedance boundary conditions. The secular equation for Rayleigh surface wave under impedance boundary conditions is derived in the explicit form. In the absence of impedance and microrotation, the secular equation reduces to classical secular equation for Rayleigh wave in an isotropic elastic half-space with traction free boundary conditions. The non-dimensional speed of propagation of Rayleigh wave is computed for an aluminium-epoxy composite as an example of a micropolar elastic solid and is shown graphically against nondimensional material constant, frequency and impedance parameters.