Guided waves in cylindrical multi-layered medium

In this paper, the dispersion characteristics and excitation mechanisms of the guided waves propagated in a cylindrical multi-layered elastic solid medium are investigated. The dispersion equation of the guided waves is generally a plural function for a real axial propagation velocity. We transform it into a real dispersion function and employ the bisection technique to find all the real roots, in order to give all the dispersion curves of the guided waves. All the guided modes propagated in two-, three-, four-, and five-layered models are studied. The excitation intensities of the guided waves excited by the symmetric point source, axial and radial force sources are studied. They are highly relied on both excitation frequency and radial position. The dominant modes are different with different excitation frequencies. Each mode reaches its maximum amplitude around the frequency where its group velocity reaches minimum and finally tends to zero at high frequency. The displacements of the guided waves have a complicated relation to the radial position too. The intensities of the Stoneley waves, which are interfacial waves propagated in cylindrical interfaces, decay with radial distance far from the interface into the outside layer, and finally approach zero at infinity. Moreover, the lowest branch of flexural guided waves excited by radial force source holds the promise for NDE of rock bolts. It can be excited out with the largest intensity in the lower frequency range. Excitation intensity and dispersion curve should be investigated together to determine whether one guided wave is suitable for NDE.