Sound transmission through a periodic cascade with application to drill pipes

Abstract

Acoustical data transmission through the wall of drill pipes is considered. Drill pipes are known to behave like bandpass filters; the position of the pass bands can be determined analytically. This work extends the frequency domain drill pipe models presented by Barnes and Kirkwood [J. Acoust. Soc. Am. 51, 1606–1608 (1972)], and more recently by Drumheller [J. Acoust. Soc. Am. 85, 1048–1064 (1989)]. The approach discussed in this paper has the advantage that it yields explicit expressions for the fine structure of the drill pipe’s frequency response in the pass bands. It furthermore allows the effect of energy dissipation and pipe segment length variations to be included in the model. The emphasis of the paper, however, lies on the time domain modeling of the drill pipe. The propagation of sound energy pulses through its wall, and the effect of multiple reflections and/or transmissions during this propagation, are described using a Markov chain. Explicit expressions result for the expected duration of an energy pulse’s trip from one end of the drill pipe to the other, depending upon the number of drill pipe segments and the transmission coefficient at the tool-joints connecting them. The results are applicable to any situation where sound or energy transmission through a cascade of acoustic components occurs.