Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mechanical Engineering & Applied Mechanics

First Advisor

Burton Paul


For us to compete in today’s global market place, industrial machines must be faster than ever before. Achieving high throughputs generally requires subjecting lightweight components to highly transient loads. Although elastic stress waves are the root cause of many failures in high-speed industrial equipment, many design engineers are reluctant to stray from the familiar static or rigid body theories. Many practical systems which are too complex for analytical wave treatment, could be analyzed by finite element analysis (FEA). However, the extremely high velocities of wave fronts in metals (e.g., 17,000 ft/sec in steel) requires the use of extremely tiny time steps in FEA, making this method slow and cumbersome for many problems.

To help bridge this gap, a digital network method is developed herein for analyzing complex, transient and steady state, one dimensional longitudinal wave problems. The algorithm implements a regularized characteristic grid network, thus it is computationally efficient, yet robust. In contrast to FEA and finite difference techniques, our method produces piecewise exact solutions of the one dimensional wave equation, thereby reducing discretization errors. A system response is determined by tracking the propagation of each discretized stress wavefront, as it is transmitted and reflected along the regularized characteristic lines.

Our method is fully capable of treating nonuniform elastic rods varied in cross sectional area, and nonuniform helical springs varied in helix diameter and pitch. New models are presented which allow generalized time dependent conditions on force, velocity, displacement or impedance, to be specified either at the boundaries or in the interior, and to permit lumped masses at such locations. Other new models are developed for external and internal viscous damping, steady state response, longitudinal impact and dynamic separation.

As a modeling tool, the digital network method provides a means of visualizing the actual phenomenon that is superior to any other method known. Comparisons with normal mode analysis provide verification of the digital network method, showing near exact agreement. Comparisons are also made with FEA solution.

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