5I-3. Guided Waves in Cylindrical Multi-Layered Medium

Propagation of guided waves in cylindrical multi-layered elastic solid medium is an interesting research topic. One important application is ultrasonic non-destructive evaluation (NDE) for inspection of the rockbolts which are installed to reinforce ground in mining and civil engineering structures. Although some studies have been reported on this topic, most of them focus on the dispersion characteristics without considering the excitation mechanisms. If one guided mode with good dispersion characteristics has less excitation intensity than other modes, it will be difficult to receive. Therefore, the excitation intensity is an important physical quantity for guided waves, yet little attention has been paid on it. In this paper, guided waves propagated in a cylindrical multi-layered elastic solid medium are studied. Not only are the dispersion characteristics analyzed further, but also the excitation mechanisms of all guided modes are investigated as keystone. 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 robustly. All the guided modes propagated in two-, three-, four-, and five-layered models are studied. Each one of the guided wave dispersion curves begins at its cutoff frequency where phase velocity is equal to the shear velocity of the outside layer. And it finally meets its high-frequency phase velocity asymptote which is either equal to the smallest shear velocity (named as Vsmin) among all the layers for the normal waves, or less than Vsmin for the Stoneley waves. The excitation intensities of the guided waves excited by symmetric point source, axial and radial force sources are investigated. They are highly relied on excitation frequency and radial position. Thus dominant modes are different with different excitation frequencies. Moreover, intensity of each mode reaches its maximum around the frequency where the group velocity reaches its minimum and finally tends to zero at high frequency. The displacement distributions of the normal waves along the radial direction are complicated. However, 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 have been investigated together to determine whether one guided wave is suitable for NDE. Moreover, primary testing results have been obtained by modeling experiments undertaken in laboratory.