Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material

The propagation of ultrasonic guided waves in an elastic hollow cylinder with a viscoelastic coating is studied. The principle motivation is to provide tools for performing a guided wave, nondestructive inspection of piping and tubing with viscoelastic coatings. The theoretical boundary value problem is solved that describes the guided wave propagation in these structures for the purpose of finding the guided wave modes that propagate with little or no attenuation. The model uses the global matrix technique to generate the dispersion equation for the longitudinal modes of a system of an arbitrary number of perfectly bonded hollow cylinders with traction-free outer surfaces. A numerical solution of the dispersion equation produces the phase velocity and attenuation dispersion curves that describe the nature of the guided wave propagation. The attenuation dispersion curves show some guided wave modes that propagate with little or no attenuation in the coated structures of interest. The wave structure is examined for two of the modes to verify that the boundary conditions are satisfied and to explain their attenuation behavior. Experimental results are produced using an array of transducers positioned circumferentially around the pipe to evaluate the accuracy of the numerical solution.