Effect of radius on propagation of surface waves in coated cylindrical cavities

Abstract

The dispersion relations of axisymmetric surface waves are studied for the inner surface of a cylindrical borehole in an isotropic elastic medium coated with a thin layer satisfying equations of motion of the Kirchhoff–Love plate model. It is shown that up to three surface waves can exist, depending on the parameters of the system, in addition to a Rayleigh-like wave that occurs independently of coating. The finite curvature radius of the cylinder results in a cut-off wave vector for each kind of waves. The cut-off for the Rayleigh-like mode turns out particularly low for sufficiently massive and distensible coatings.

Keywords:

• true surface waves
• dispersion relations
• borehole
• Kirchhoff–Love plate
• cut-off frequency

Acknowledgements

This work was supported by Krakowskie Konsorcjum ‘Materia-Energia-Przyszłość’ im. Mariana Smoluchowskiego as a part of KNOW 2012-2017, KKS123/8-09985.