Coupled extensional and bending motion in elastic waveguides

Abstract

A variety of different linear elastic waves propagate in long slender rods. These waves do not interact in straight rods; however, extensional and bending waves do interact in slightly curved rods. If curved rods are used as waveguides for extensional waves, wave energy is exchanged between extensional and beding waves. The result has the superficial appearance of viscous attenuation. The petroleum and geothermal industries have an interest in using drill pipe as a waveguide to transmit data by acoustic waves. Attempts have been made to transmit data from transducers in the vivinity of a drill bit to the drill rig at the surface. These efforts have not been successful. Poor signal strenght is a major problem. Historically,the observed reduction in signal strength is attributed to viscous dissipation. This paper proposes an alternative model-mode conversion from extensional waves to bending waves. This model is analyzes both as an eigenvalue problem and a transient finite-difference problem. The results predict measured attenuation levels, and account for many anomalous observations.