Mechanical Engineering Oepartment Exhibition Road, London SW7 2BX INTROOUCTIONThe application of guided waves in NOT can be hampered by the Iack of readily available dispersion curves for complex structures. To overcome this hindrance, we have developed a general purpose program that can create dispersion curves for a very wide range of systems and then effectively communicate the information contained within those curves. The program uses the global matrix method to handle multi-layered Cartesian and cylindrical systems. The solution routines cover both leaky and non-leaky cases and remain robust for systems which are known to be difficult, such as !arge frequency-thicknesses and thin layers embedded in much thicker layers. Elastic and visco-elastic isotropic materials are fully supported; anisotropic materials are also covered, but are currently limited to the elastic, non-leaky, Cartesian case.An extremely !arge amount of work has already been clone to describe the wave propagation in layered systems, which began in the late nineteenth century and continues today There is not enough space in this paper to describe the contributions that many excellent researchers have made to the field. Instead, this paper describes how we have combined some of this previous work and our own research to create a robust, user friendly, general purpose tool. A review of matrix techniques as they apply to modelling ultrasonic waves in multi-layered media is given in (1).When creating dispersion curves, the displacements and stresses for each type of material and geometry are described in a materiallayer matrix. By satisfying the given boundary conditions at each interface, the individuallayer matrices are assembled to describe the behaviour of the entire system. The dispersion curves then emerge as solutions to the assembled system of equations.Once the dispersion curves are generated, our program provides many easy methods to explore and use the information contained within the curves. A mode shape display continually updates the distribution of stresses, displacements, and energy as points are selected on a dispers10n curve. The phase velocity, group velocity, attenuation, real wave-number, angle of incidence, etc. can be shown and compared. In addition, an interface to our finite element program allows the interaction of gutded waves with defects to be examined.The program has been developed as a by-product of our research. It has proven to be a valuable tool for understanding wave propagatwn in complex systems and transferring that understanding to new ultrasomc testwg applications

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The dispersion relationships of a system comprising a circular bar imbedded in a solid medium having a lower acoustic impedance than the bar have been predicted. A generic study of such systems has been undertaken, motivated by a particular interest in the case of a circular steel bar imbedded in cement grout which has application to the inspection of tendons in post-tensioned concrete bridges; measurements to confirm the predictions have been carried out for this case. The attenuation dispersion curves show a series of attenuation minima at roughly equal frequency spacing. The attenuation minima occur at the same frequencies as energy velocity maxima and they correspond to points at which the particle displacements and energy of the particular mode are concentrated towards the center of the bar so leakage of energy into the imbedding medium is minimized. The attenuation at the minima decreases with increasing frequency as the energy becomes more concentrated at the middle of the bar, until the material attenuation in the bar becomes a significant factor and the attenuation at the minima rises again. For the particular case of a steel bar in cement grout, the minimum attenuation is reached at a frequency-radius product of about 23 MHz-mm. The frequency-radius product at which the minimum attenuation is reached and the value of the minimum attenuation both increase as the acoustic impedance of the imbedding medium increases.

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