Implementation of the ultrasonic second harmonic generation has typically been restricted to simple setups such as through-transmission or Rayleigh surface waves. Recent research has evaluated the second harmonic generation in P- and SV- waves reflected from a stress-free surface to enable the single-sided interrogation of a specimen. This research considers the second harmonic generation in an aluminum specimen, which is analytically evaluated using an approach based on the perturbation method. Here, the model is chosen to mimic an experimental setup where a longitudinal wave is generated at an oblique angle and the reflected wave is detected using a set of wedge transducers. Due to mode conversion at the interface of the wedge and the specimen, it is necessary to evaluate longitudinal and shear waves, determining all second harmonic waves generated in the bulk and at the stressfree boundary. The theoretically developed model is then implemented in a commercial finite element code, COMSOL, using increasing fundamental wave amplitudes for different values of third order elastic constants. The results of this computational model verify the analytical approach and the proposed measurement setup, taking into account assumptions and approximations of the solution procedure. Furthermore, the computational model is used to draw important conclusions relevant to the experimental setup, including the need to avoid evolving surface waves and interactions with diffracted waves. These numerical results are used to develop a recommendation for the measurement position and incident angle. Finally, the nonlinearity of two different aluminum specimens is measured with the suggested measurement setup and the results confirm the feasibility of the single-sided determination of the acoustic nonlinearity using reflected bulk waves.

This research investigates wave propagation in an elastic half-space with a quadratic nonlinearity in its stress-strain relationship. Different boundary conditions on the surface are considered that result in both one- and two-dimensional wave propagation problems. The goal of the research is to examine the generation of second-order frequency effects and static effects which may be used to determine the nonlinearity present in the material. This is accomplished by extracting the amplitudes of those effects in the frequency domain and analyzing their dependency on the third-order elastic constants (TOEC). For the one-dimensional problems, both analytical approximate solutions as well as numerical simulations are presented. For the two-dimensional problems, numerical solutions are presented whose dependency on the material's nonlinearity is compared to the one-dimensional problems. The numerical solutions are obtained by first formulating the problem as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. In the one-dimensional cases, it is shown that the analytical and numerical solutions are in good agreement with each other, as well as how different boundary conditions may be used to measure the TOEC. In the two-dimensional cases, it is shown that there exist comparable dependencies of the second-order frequency effects and static effects on the TOEC. Finally, it is analytically and numerically investigated how multiple reflections in a plate can be used to simplify measurements of the material nonlinearity in an experiment.