# Expressions to Rayleigh circumferential phase velocity and dispersion relation for a cylindrical surface under mechanical pressure

Article

## Abstract

This paper describes a substantiated mathematical theory for Rayleigh waves propagated on some types of metal cylinders. More specifically, it presents not only a new way to express the dispersion relation of Rayleigh waves propagated on the cylindrical surface, but also how it can be used to construct a mathematical equation showing that the applied static mechanical pressure affects the shear modulus of the metal cylinder. All steps, required to conclude the process, consider the equation of motion as a function of radial and circumferential coordinates only, while the axial component can be overlooked without causing any problems. Some numerical experiments are done to illustrate the changes in the Rayleigh circumferential phase velocity in a metal cylindrical section due to static mechanical pressure around its external surface.

### Keywords

Phase velocity Dispersion relation Rayleigh waves Curved surface

### Mathematics Subject Classification

Primary 74J15 Secondary 00A69

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