Rayleigh Waves in Anisotropic Crystals Rotating About the Normal to a Symmetry Plane

Abstract

The propagation of surface acoustic waves in a rotating anisotropic crystal is studied. The crystal is monoclinic and cut along a plane containing the normal to the symmetry plane; this normal is also the axis of rotation. The secular equation is obtained explicitly using the "method of the polarization vector", and it shows that the wave is dispersive and decelerates with increasing rotation rate. The case of orthorhombic symmetry is also treated. The surface wave speed is computed for 12 monoclinic and 8 rhombic crystals, and for a large range of the rotation rate/wave frequency ratio.

Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions

“…In the absence of impedance parameters (that is for traction free boundary), the present secular equation (15) is in agreement with that obtained by Destrade (2004a, 2004b). The secular equation obtained by Vinh and Ogden (2004, 2005) can be recovered from the present secular equation (15) when we neglect both rotation and impedance parameters.…”

“…The secular equation obtained by Vinh and Ogden (2004, 2005) can be recovered from the present secular equation (15) when we neglect both rotation and impedance parameters. In the absence of impedance parameters only, the present numerical results for Rayleigh wave speed can be verified from the results obtained by Destrade (2004a, 2004b). After neglecting the rotation and impedance parameters, the present numerical results of Rayleigh wave speed also agrees with those shown by Vinh and Ogden (2005).…”

“…However, Vinh and Hue (2014) have not solved the secular equation for the Rayleigh wave speed. For Ω 0 = 0, the present numerical results will act as the numerical solutions for secular equation given by Vinh and Hue (2014).In the absence of impedance parameters (that is for traction free boundary), the present secular equation (15) is in agreement with that obtained by Destrade (2004a, 2004b). The secular equation obtained by Vinh and Ogden (2004, 2005) can be recovered from the present secular equation (15) when we neglect both rotation and impedance parameters.…”

“…Collet (2003) has studied the propagation of Rayleigh waves over an elastic anisotropic half-space rotating at a constant angular rate about a symmetry axis using the first integrals. Destrade (2004a) has studied the propagation of surface acoustic waves in a rotating monoclinic crystal cut along a plane containing the normal to the symmetry plane and has obtained explicit secular equation using the method of polarization vector. Destrade (2004b) has also studied the propagation of Rayleigh surface waves over a rotating orthorhombic crystal.…”

Surface acoustic waves in rotating orthorhombic crystals

“…The case where the orthorhombic crystal rotates about an axis orthogonal to the direction of propagation and to the normal to the free surface has been treated elsewhere (Destrade 2003) as a special case of a monoclinic crystal. It turns out that the in-plane strain decouples from anti-plane strain, and that the displacement is of the form,…”