Wave guides

A new analytical method based on the wave propagation scheme has been developed for the dynamic analysis of axially symmetric shells with arbitrary boundary conditions and interior supports. In this approach, a shell structure is considered as a waveguide and the response to external excitations is treated as a superposition of wave motions. To segregate the effect of the interior supports, the waveguide is first divided into several sub-waveguides. Upon analyzing these sub-waveguides separately, a composition scheme is adopted to relate them by connecting the wave components according to the continuity conditions for the state variables at each interior supports. Closed form solutions for free and random vibration are derived. The proposed method is presented in a general fashion and numerical examples are given to illustrate the application of the theory.

In this thesis, discretized finite element equations were derived and applied to the solution of electromagnetic fields in homogeneous and inhomogeneous waveguides. To improve the accuracy of the results several approaches were taken. Higher order elements were first introduced in the finite element formulation, then a penalty function was applied with explicit boundary conditions, which limit the appearance of nonphysical solutions. The results obtained from the finite element analysis were compared to analytical results when available and found to be very accurate.

In this dissertation, the Radar Cross Section (RCS) of a large periodic array of rectangular open-ended waveguide apertures is determined numerically using several methods. The aperture boundaries are presumed to be Perfect Electrical Conductors (PEC). Although the problems of radiation from such a waveguide array and of aperture array scattering have been treated in the literature, the problem of scattering from an array of waveguide apertures does not appear to have been solved before. Considering the case of an array with constituent guides of semi-infinite length, the RCS is computed by several numerical methods based on the Integral Equation (IE) method, a least-squared error minimization technique referred to as Squared Field Error (SFE) method, direct solution of a surface integral equation, the Spectral Domain Method, and by using waveguide modes computed via the Finite Element Method (FEM). The case of finite-length guides is also treated using the IE and SFE methods. The results of these methods are compared with experimental data obtained from an outdoor RCS range. In order to simulate the semi-infinite case, the finite-length waveguides were terminated with radar absorbing foam so that nearly all reflection occurred at the apertures impinged upon by the incident plane wave. For all the methods cited, the infinite array approximation (cell-to-cell field periodicity except for a linear progressive interelement phase shift) is assumed to hold. A derivation of Floquet modes which implement this "phase-periodic" boundary condition is provided in an appendix, where an incidental discussion concerning the scalar and vector Laplacian operators is also furnished. A description of the structure and user interface of the software which has been written to implement the various methods is also given. The purposes of major subroutines and data structures are also delineated and several control-flow diagrams are included. As a foundation to extend the present work to analysis of the electromagnetic fields within an absorber coated PEC waveguide, a brief survey and a discussion of related work is provided.