This thesis is concerned with the study of two independent problems. Chapter 2 is devoted to the development of a new representation for the dynamic Green's tensor for a layered medium. No completely closed solution is possible and the objective here is to develop a representation that is more amenable to computation than the existing representations (Cagniard (39), Willis (73)). The representation derives from a reduction of the integrals required for the inversion of the terms in a "generalized ray" series. For the three-dimensional (point source) problem the final solution requires either a single integration (isotropic layers) or two integrations (anisotropic layers) over contours that are independent of time t and position x. The integrand is a simple explicit function, much of which is independent of x and t and may be tabulated when the solution is required for a range of values of x and t. The remainder of this thesis examines the time-harmonic response of thin, elastic, fluid-loaded plates stiffened by attached parallel beams. The sound radiated by such structures has been studied by many authors but few have been concerned with the motion of the plate. Chapters 3, 4 and 5 of this thesis examine plates stiffened, respectively, by finite, infinite, and semi-infinite arrays of beams. In chapter 3, Fourier transforms are used to obtain a set of simultaneous equations for the transformed displacements and rotations at the beams. The inverse transform of the solution to this set of equations is evaluated asymptotically. In chapters 4 and 5 the stiffening beams are equally spaced. The equations are formulated in terms of discrete convolutions and a transform, related to the modified Z-transform, is used (together with the Wiener-Hopf technique in chapter 5) to obtain the solution. Asymptotically, the motion of the stiffened regions of the plate has the form of a Floquet wave.
|Date of Award||1981|