| Ultrasonic wave propagation in solids is a subject of fundamental interest for quantitative nondestructive evaluation and material characterization. Theoretical and experimental studies of ultrasonic waves and their applications to engineering and biomedical imaging have been actively pursued in recent years. Modeling of laser-generated thermoelastic waves is the subject of this dissertation. The objective is to provide a rigorous analysis of laser generated guided ultrasonic waves in anisotropic plates. Characteristic features such as dispersion of thermoelastic waves and transient response of plates are investigated and the influence of different factors on these features are critically examined. Fundamentally, thermoelastic wave propagation in elastic solids is governed by two basic equations, namely, elastodynamic (including thermal strain) and thermal wave. In plates, both elastodynamic and thermal waves are dispersive because of constructive interference of multiply reflected waves at the plate boundaries. Different modeling techniques have been employed here to derive the dispersion relations and frequency spectra for an anisotropic homogenous elastic thermally conducting plate. First, an exact approach in which the governing equations are rewritten in terms of potential functions, is introduced. This approach is valid for a plate with transverse isotropy. On the other hand, the second exact approach is applicable to any monoclinic material. In this approach, the governing equations and boundary conditions are recast in a matrix form and the resulting eigenvalue problem is solved. Solving this problem and applying appropriate boundary conditions yields the dispersion relations of the plate. Thirdly, a semi-analytical finite element method (SAFEM) is also introduced. In this approach, which is applicable to any anisotropic material, the plate is discretized along its thickness using N parallel and homogeneous layers. The fourth approach is an approximate one. In this, a first order plate theory is developed to obtain the dispersion relations for the lowest longitudinal elastic and thermal modes. Transient response of a plate due to a laser pulse is also investigated in this dissertation. Two different approaches are employed as well. The first one is based on the aforementioned SAFEM method. The other one is an exact one. Very good agreement between the two predictions is observed. The temporal and spatial distributions of the laser pulse are modeled. The transient results are found to be in qualitative agreement with experiments. |
