Time-domain computations of one-dimensional elastic waves in liquids, solids and ferroelectric ceramics

Computational solutions of linear-elastic wave equations are usually executed with frequency-domain algorithms; however, time-domain methods offer significant advantages in speed and simplicity. In this work, a time-domain algorithm is developed for one-dimensional problems in rectangular, cylindrical, and spherical coordinates. The result is simultaneously a finite-difference and method-of-characteristics algorithm. For most materials, the algorithm is explicit — for a given time, the solution at a particular position depends only upon solutions at earlier times. The exceptions are the ferroelectric ceramics which are an important class of electromechanical transducers. For these materials, the algorithm is implicit — for a given time, the solution at a particular position within the ceramic depends not only upon solutions at earlier times but also upon the current solutions at all other positions within the ceramic. Application of the algorithm is demonstrated for a variety of problems. Solutions are compared to the conventional finite-difference method, the conventional method of characteristics, and the Laplace transform method. Practical applications include the analysis of a lithotripter tool for fragmenting human kidney stones, and an acoustic logging tool for measuring the diameter and thickness of well casing.