Mechanical Engineering ETDs

Publication Date

Fall 8-6-1970


This dissertation describes solution of a class of problems of three dimensional (non-symmetrical) elastic wave propagation in bodies of revolution. The method of analysis is expansion into circumferential modes followed by solution of an approximate numerical scheme using a digital computer. The material constituting the body has been assumed homogeneous, isotropic, linearly elastic and only one mate­rial may appear in the body. A load may be applied either by a pressure blast or by a target body acting over some portion of the boundary. The loading functions may vary around the circumference. Three dimensional wave motion is analyzed by expanding all dependent variables in Fourier series in the circumferential direction.

Difference equations are derived by finite difference methods. A numerically defined orthogonal coordinate sys­tem is introduced to handle arbitrary body geometries. Solutions are advanced in time by a modified leap-frog scheme with spatial derivatives approximated by centered differences.

Two specific problems are solved. In both cases a solid cylinder with a traction free lateral boundary is analyzed. In-the first problem velocity is prescribed on the impact surface while in the second one traction is prescribed. A range of stability is ascertained for these two problems for various circumferential modes. Initial results are obtained to describe the dispersion of higher modes.

The method successfully solves the problems attempted in a reasonably short execution time (5 x 10)4 seconds/mesh point-cycle on CDC6600 computer). FORTRAN programs are written to allow solution of more complex geometrics, such as hollow cylinder, plates, hollow cylinders with end caps, transition regions, etc., and require few changes to solve such problems.

Degree Name

Mechanical Engineering

Level of Degree


Department Name

Mechanical Engineering

First Committee Member (Chair)

Frederick D. Ju

Second Committee Member

Bohumil Albrecht

Third Committee Member

Lawrence Fred Shampine

Fourth Committee Member


Document Type