Investigation and application of nonlinear ultrasonic guided wave in closed and open waveguides

Nonlinear ultrasonic guided waves, combining the advantages of nonlinear ultrasound and ultrasonic guided waves, are interesting for Non-Destructive Testing (NDT) since they are sensitive to incipient damage as well as offering the potential for rapid inspections of large structures. For waveguides with regular cross sections, e.g. plates, rods or pipes, analytical solutions can be obtained to study the nonlinear guided wave propagation. For waveguides with arbitrary cross sections, numerical methods are usually used due to the complexity to solve nonlinear Navier equation analytically with arbitrary boundary conditions. All above waveguides are commonly called closed waveguides, where energy of the wave only concentrates in the waveguides. Nonlinear ultrasonic guided waves have been investigated widely in closed waveguides, especially in regular waveguides. However, it will be more challenging when the waveguides are embedded/immersed in another medium (usually called open waveguides), where interaction between the waveguides and the surrounding material may lead to energy leaking away from the waveguides, which makes the description of nonlinear ultrasonic guided waves even more challenging for open waveguides. Studies of nonlinear ultrasonic guided waves in open waveguides require understandings of modal properties of these structures. A number of analytical or numerical models have been developed to understand the behavior of guided waves in open waveguides, among which one of the attractive methods is to combine the Semi-Analytical Finite Element (SAFE) method with Perfectly Matched Layer (PML). But most of the studies on SAFE-PML method focus on embedded cases, which only contain solid medium, and most of them are based on specific Finite Element (FE) codes that are not accessible to public and time consuming to develop. In this thesis, SAFE-PML method is developed for both embedded and immersed waveguides, and implement it into a commercial FE package. As no source code is required, the presented method will be attractive to a wide range of researchers in NDT. This method is first demonstrated and validated in two cases with analytical solutions. It is then applied to practically important problems, showing the potential of the method. The properties of nonlinear ultrasonic guided waves in open waveguides are investigated. Mathematical framework is first established based on real reciprocity relation and modal expansion with PMLs. Numerical models are then implemented, including nonlinear SAFE method to predict the properties of nonlinear ultrasonic guided waves, and time domain FE models to simulate the nonlinear guided wave propagation and cross validate the predictions from nonlinear SAFE method. Two examples, an aluminum plate attached to an elastomer and an aluminum plate with water-loaded on one side are studied to demonstrate the proposed methods and reveal some interesting phenomena that only exist in open waveguides. It is interesting to find that the amplitude of the attenuated second harmonic wave (SHW) in immersed waveguides can become constant with propagation distance, only if the primary wave is non-leaky, which may bring potential NDT applications for underwater inspections. Such feature is also validated by well-designed experiments in immersed plates. This thesis also explores the possibility to use low frequency symmetric Lamb mode (S0) for nonlinear applications, as the widely used internal resonant Lamb mode pair (S1, s2) suffers from two associated complications: inherent dispersive and multimode natures. At low frequency region, the S0 mode shows little dispersivity and it is easier to generate pure S0 mode. Also, the secondary mode grows linearly in a significant distance. Numerical modelings including the nonlinear SAFE method and time domain FE models, as well as experiments are used to validate the nonlinear features and therefore demonstrate an easy alternative for nonlinear Lamb wave applications.Doctor of Philosoph