A digital network method for one dimensional wave propagation in nonuniform elastic rods and helical springs
A digital network method is developed for analyzing complex, transient and steady state, one dimensional longitudinal wave problems. The algorithm implements a regularized characteristic grid network, which is computationally efficient, yet robust. The 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 theoretical modeling tool, the digital network method provides a means of visualizing the actual phenomenon that is superior to any other method known to us. The digital network method was verified against normal mode solutions, showing virtually perfect agreement. For comparable accuracies, the normal mode solution required far greater computational and analytical effort. Excellent agreement was also demonstrated with finite element analysis of a highly tapered rod subjected to high frequency (30 KHz) loading and initial condition transients.
DeAngelis, Dominick Albert, "A digital network method for one dimensional wave propagation in nonuniform elastic rods and helical springs" (1995). Dissertations available from ProQuest. AAI9532162.