Guided waves hold great potential for applications in the field of ultrasonic nondestructive testing. Examples of possible applications are the ultrasonic testing and structural health monitoring of wheelset-axles as used in trains. Depending on the particular type, these axles can be described as either thick cylindrical rods or thick walled hollow cylinders with varying thickness. Wheelset-axles are safety relevant components that have to be inspected on a regular basis. The use of guided waves would allow a full inspection while accessing only the front faces of the axle, thus potentially speeding up the inspection procedure. In order to develop such an inspection technique, however, detailed knowledge of wave propagation through the axle is required. Established mesh-based procedures, like the finite element method, could be used to simulate guided wave propagation in such structures. However, due to the size of the axle itself and the comparatively fine mesh that is dictated by the wavelengths usually applied in ultrasonic testing, these mesh-based procedures would be very expensive in terms of computation times. The multimodal approach seems to be a very promising alternative that can be expected to provide results significantly faster. The multimodal method uses the guided wave modes of a corresponding waveguide with a constant cross-section as basis in which the local sound field at any given position in a waveguide with varying thickness can be expressed. Thereby the numerical effort is reduced to solving the one dimensional differential equations that govern the evolution of the coefficients in the mode spectrum along the waveguide. Once the sound field has been calculated, a time dependence can easily be included, which allows the simulation of pulse propagation through the waveguide. In this thesis, the multimodal approach, as described for the calculation of Lamb-waves in plates with non-constant thickness, is extended to other types of elastic waveguides such as cylindrical rods and thick walled hollow cylinders. For the sake of simplicity, investigations are restricted to axially symmetric wave modes. The results obtained with the multimodal approach are validated against FEM-simulations. It is shown that the multimodal method potentially holds a great advantage in terms of computation time over commercially available software based on the finite element method. Finally, the multimodal method is evaluated with respect to possible future applications on wheelset-axles.
Guided waves are increasingly a subject of great interest in nondestructive testing. An example of research in this field is the development of a novel procedure for ultrasonic testing of wheelset-axles using guided waves, which requires to treat the wheelset-axle as a thick walled cylinder with varying thickness. In order to describe ultrasound propagation in a waveguide with non-constant thickness, a multimodal approach, which allows to avoid extensive mesh-based numerical calculations, seems to be promising. The method treats the modes of a corresponding waveguide with constant thickness as a base in which an arbitrary sound field can be expressed. Since the local sound field at any given position in the waveguide with varying thickness will be a combination of these base modes, the problem is reduced to solving the differential equation that governs the evolution of the coefficients in the mode spectrum along the waveguide. Once the description of the sound field along the waveguide is obtained, the time dependence is added by multiplication with a simple oscillating term. Simulations of pulse propagation through the waveguide can then be constructed by adding up a sufficient number of mono-frequent continuous wave solutions. As an early stage in developing a simulation tool for sound propagation in thick walled cylinders with varying thickness, the multimodal approach was implemented and tested for the simple case of plate geometries. In this work, an overview of the simulations carried out for plates with non-constant thickness is presented. The performance of the algorithm based on the multimodal approach and the obtained results are compared to those of mesh-based simulation tools.
In this paper, a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures is presented as an alternative to the currently established numerical procedures. The method is based on a spectral decomposition into eigenfunctions of the Laplace operator on the cross-section of the waveguide. This translates the calculation of real or complex wave numbers at a given frequency into solving an eigenvalue problem. Cylindrical rods and plates are treated as the asymptotic cases of cylindrical structures and used to generalize the method to the case of hollow cylinders. The presented method is superior to direct root-finding algorithms in the sense that no initial guess values are needed to determine the complex wave numbers and that neither starting at low frequencies nor subsequent mode tracking is required. The results obtained with this method are shown to be reasonably close to those calculated by other means and an estimate for the achievable accuracy is given.