COINCIDENCE OF THERMOELASTIC AND THERMOVISCOUS ACOUSTIC WAVES IN FLUID-FILLED ELASTIC TUBES

Abstract

Thermoelastic and thermoviscous acoustic wave propagation in fluid-filled steel tubes is studied using the exact three-dimensional (3-D) fluid-elastic coupled system equations for the vibration in the n=0 and 1 circumferential modes. Water- and air-filled tubes are examined. The water-filled steel tube shows a strong fluid–elastic coupling effect in the lower frequency range and the air-filled tube shows a strong thermal effect for all frequencies. An 88·9 mm outer diameter tube with 3·05 mm wall thickness is used for the study. Due to the fluid–elastic coupling introduced for air having a specific heat ratio of 1·4 (the solution uncouples when the ratio is 1·0), thermal effects are seen to be very important with the modal attenuation rate being at least 32% underestimated if the thermal effect is not included in the air–steel system. A coincidence phenomenon is accurately found directly from the coupled modes in the fluid–elastic coupled system. When coincidence occurs, the axial modal attenuation rate drops sharply, allowing the exact determination of the coincidence frequency by locating the local minimum of the modal spatial attenuation rate with increasing frequency. In the water–steel system, the coincidence frequency is seen to be 8% in error if methods are employed using the uncoupled theory for the separate fluid and elastic wall.