Abstract
For three dimensional vibration analysis of piping system containing fluid flow, a transfer matrix formulation is presented. The fluid velocity and pressure were considered, that coupled to longitudinal and flexural vibrations. Transfer matrices were derived from direct solutions of the differential equations of motion of pipe conveying fluids, and the variations of natural frequency with flow velocities for straight and curved pipes were investigated. The results were confirmed to the corrections of known data. The scheme of this study can be easily applied to the related fields, using small size personal computers with core memory about 200kbytes.
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References
Benjamin, T. B., 1961, “Dynamics of System of Articulated Pipes Conveying Fluid, Parts I, II”,Proc. of Royal Society (London), Ser. A 261, pp. 457–486
Blevins, R. D., 1990, Flow-Induced Vibration, 2nd ed., Van Nostrand Reinhold Co., pp. 384–414
Chen, S. S., 1972, “Vibration and Stability of a Uniformly Curved Tube Conveying Fluid,”J. Acoust. Soc. Am., Vol. 51, No. 1, Part 2, pp. 223–232
Chen, S. S., 1973, “Out-of-Plane Vibration and Stability of Curved Tubes Conveying Fluid,”J. of Applied Mechanics, Trans. ASME, June, pp. 362–368
El-Raheb, M., 1981, “Vibrations of Three-Dimensional Pipe System with Acoustic Coupling,”J. of Sound and Vibration, Vol. 78. No. 1, pp. 39–67
Everstin, G. C., 1986, “Dynamic Analysis of Fluid-Filled Piping Systems Using Finite Element Techniques,”J. of Pressure Vessel Technology, Trans. ASME, Vol. 108, Feb., pp. 57–61
Gregory, R. W. and Paidoussis, M. P., 1966, “Unstable Oscillation of Tacular Cantilevers Conveying Fluid: I., II,” Proc. of Royal Society (London). Ser. A 293, pp. 512–527
Hong S. C., Park, C. H. and Kim, T. L., 1991. “Out of Plane Vibration of Angled Pipes Conveying Fluid,”J. of the Korean Nuclear Society, Vol. 23, No. 3, pp. 306–315
Housner, G. W., 1952, “Bending Vibrations of a Pipe Line Containing Flowing Fluid”,J. of Applied Mechanics, Trans. ASME, June, pp. 205–208
The Kellogg, M. W. Co., 1956,Design of Piping Systems, John Wiley & Sons, INC., pp. 257–294
Kohli, A. K. and Nakra, B. C., 1984, “Vibration Analysis of Straight and Curved Tubes Conveying Fluid By Means of Straight Beam Finite Elements,”J. of Sound and Vibration, Vol. 93, No. 2, pp. 307–311
Lee, Y. S. and Chun, I. H., 1991, “Vibration Characteristics of Pipe Element Containg Moving Medium by a Transfer Matrix,”KSME in Korea, Vol. 15, No. 1, pp. 366–375
Lenmez, M. W., Wiggert D. C. and Hatfield, F. J., 1990, “Modal Analysis of Vibrations in Liquid Filled Piping Systems,”J. of Fluids Engineering, Trans. ASME, Vol. 112, Sep., pp. 311–318
Park, C. H., Lee, U. S., Hong S. C. and Kim, T. L., 1991, “Stability Analysis of Piping System Conveying Unsteady Flow,”KSME in Korea, Vol. 15, No. 5, pp. 1512–1521
Pestel, E. C., Leckie, F. A., 1963,Matrix methods in Elastomechanics, McGraw- Hill, Book Co., New York, pp. 51–204
To C. W. S. and Kaladi, V., 1985, “Vibration of Piping Systems Containing a Moving Medium,”J. of Pressure Vessel Technology, Trans. ASME, Vol. 107, Nov., pp. 344–349
Unny, T. E., Martin, E. L. and Dubey, R. N., 1970, “Hydroelastic Instability of Uniformly Curved Pipe-Fluid Systems,”J. of Applied Mechanics, Trans. ASME, Sep., pp. 817–822
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Lee, D.M., Choi, M.J. & Oh, T.Y. Transfer matrix modelling for the 3-dimensional vibration analysis of piping system containing fluid flow. KSME Journal 10, 180–189 (1996). https://doi.org/10.1007/BF02953657
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DOI: https://doi.org/10.1007/BF02953657