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The flow at incidence to a slender delta wing with leading edge and secondary separation is considered. A potential flow model is constructed in which the spiral vortex sheets of the actual flow are replaced by concentrated vortices and flat vortex feeding sheets connecting them with the separation lines. The problem is then reduced to a two-dimensional one by the use of slender body theory and the assumptions of conical flow. The method of conformal mapping is employed to obtain the potential solution. The auxiliary boundary condition on each of the vortex systems is that it is force free. The resulting non-linear algebraic equations are solved numerically by means of an iterative method, and values for lift are obtained as a function of incidence. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A modified vortex lattice method is developed to solve for the nonlinear three-dimensional unsteady incompressible flow over delta wings. Symmetric motions (pitching, heaving) and asymmetric motions (roll, yaw) are considered. Then the method is generalized to treat the nonlinear three-dimensional steady flow for bodies and wing body combinations. Numerical examples include variety of shapes and comparison with existing experimental data and other numerical methods over a wide range of angle of attack shows good agreement. For bodies alone the results deteriorate downstream of the separation region, while for wing-body combinations the agreement with the experimental data is good as long as the body separation effect is not large. The developed computer codes should provide a useful tool in the design of aircraft and missiles. / Ph. D.

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This work is the first 3-D continuum study of the free vibration of skewed and simultaneously skewed and twisted, cantilever parallelepipeds. The purpose of this study is to make available in the literature an enlarged data base of natural frequencies of these practical problems for researchers and design engineers to draw upon. The Ritz method is used to determine approximate natural frequency data. The total potential energy of the parallelepipeds is formulated using the three-dimensional theory of elasticity. The three orthogonal displacement components (u,v,w) are each approximated by finite triple series of simple algebraic polynomials with arbitrary coefficients (which are determined by applying the Ritz method). All terms of the series are constructed to satisfy the geometric boundary conditions at the fixed end of the parallelepiped. No other kinematic constraints are imposed in this analysis. Hence, the finite series of algebraic polynomials are both admissible and "mathematically complete" (75). Several convergence studies of natural frequencies are conducted on cantilever parallelepipeds. Effects of geometrical parameters such as side ratio, thickness ratio, skew angle, and twisted angle are presented in the form of nondimensional tables and graphs. Accuracy of solution method is substantiated through comparison with existing rectangular, skewed, and twisted plate results. The central focus of these comparisons are to verify the correctness and accuracy of free vibration data obtained by investigators using classical plate theories and two- and three-dimensional finite element methods.

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