Natural frequencies of tube vibration

In flow-induced vibration design of heat exchanger tube bundles, resonant conditions must be suppressed by ensuring separation of natural frequencies of the tubes and exciting frequencies (Shin & Wambsganss,1975). A number of techniques are available for computing natural frequencies of straight, curved, single and multiple span tubes. These tubes may be subjected to varying end conditions. Loose baffles act like "kinfe-edged rings" supports (Timoshenko, 1955) . Tubes are rigidly fastened to the tube sheet and supported at intermediate points along their lengths by baffles or support plates. Some tubes in the centre may be supported by every baffle, whereas tubes that pass thorough baffle window may be supported by every second and third baffle. Table 5 (MacDuff & Feglar, 1957, Kissel, 1977) gives some of the formulas/techniques for estimating the natural frequencies of straight-and curved-or U-tubes.