Solution of One-Dimensional Elastic Wave Problems by the Method of Characteristics

Abstract

A number of elastic wave problems which involve one space variable are treated, in a unified manner, by a system of second-order hyperbolic partial differential equations, with the generalized displacements as dependent variables. This system of n equations is analyzed by the method of characteristics yielding closed-form equations for the physical characteristics, the characteristic equations, and the propagation of discontinuities. Procedures for numerical integration along the characteristic curves are established. Among the elastic wave problems that may be represented by this unified approach are the Timoshenko beam, plates, bars, and sheets; in all cases, the media may be non-homogeneous. Various approximate shell equations also may be represented. Results of numerical calculations are in agreement with those obtained by other methods.