Extensional stress waves in one-dimensional elastic waveguides

Computations of linear, one-dimensional wave propagation problems are often accomplished with integral transform methods. Time-domain approaches that usually involve a infinite-difference or method-of-characteristics approach have usually been reserved for nonlinear problems. However, time-domain algorithms have unique advantages for many problems with complex combinations of geometry, internal energy sources, and boundary conditions. One such algorithm will be examined in this work. It was originally developed for an unusual waveguide problem - acoustical wave transmission through drill strings that are used to drill geothermal and petrochemical wells. The development of this algorithm takes advantage of a unique property of the linear problem. The result is a computational method that is a combination of the finite-difference and characteristics methods. A variety of example problems are treated in this work. They involve linear elastic, ferroelectric, and fading-memory materials. Examples are given of solutions to the coupled mechanical and electrostatic field equations, and to problems with nonhomogeneous material properties. 6 refs., 19 figs., 7 tabs