Ultrasonic standing wave modes in axially stressed rods

Abstract

Ultrasonic propagation in axially stressed metal resonators is examined from the standpoint of a propagating plane wave model. The theoretical results are compared with experimental data obtained with a new resonant instrument called an Ultrasonic Bolt Tensioning Monitor, capable of resolving changes in stress of less than 104 Pa (1 lb./in.2). The applied load produces a coupling to the acoustic resonant modes via a stress induced strain as well as a stress induced change in sound velocity. The coupling is shown to produce a linear relationship between load and resonant frequency characterized by a continuous wave stress acoustic constant R. Some geometrical considerations may impact R and are considered. For example, non-parallelism is shown to have produced a severe degradation of signal for conventional transducers, and the accompanying stress gradients alter the value of R. Also, the percentage of length actually under load changes R and is shown to produce an effect predicted by the plane wave model. In addition to the linear data obtained with the ultrasonic tension instrument, spectral characteristics of the samples are presented.