A Time History Method for Analysing Operational Piping Vibrations


Vibration failure of piping is a serious problem and a matter of concern for safety and reliability of plant operations. Fatigue is the main cause of such failures. Due to the complexity of the phenomenon no closed form design solutions are available. In our study an analytical technique based on the theory of vibrations in the time domain has been presented. Using the inverse theory, the problem has been reduced to a system of Volterra Integral equations to be solved simultaneously at every time step. The solution of the inverse problem may be used in the conventional method to calculate stresses and end reactions which are important from the perspective of engineering design and condition monitoring. The method is robust, simple and can be easily adopted by practicing engineers.

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S. Saha, "A Time History Method for Analysing Operational Piping Vibrations," World Journal of Mechanics, Vol. 2 No. 6, 2012, pp. 325-333. doi: 10.4236/wjm.2012.26038.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] W. G. Garrison, “Major Fires and Explosions Analyzed for 30-Year Period,” Hydrocarbon Processing, Vol. 67, No. 9, 1988, pp. 115-122.
[2] C. W. Groetsch, “Inverse Problems in Mathematical Sciences,” Vieweg Publishing, Wiesbaden, 1993.
[3] V. Komornik and P. Loreti, “Fourier Series in Control Theory,” Springer Inc., New York, 2005.
[4] D. D. Ang, R. Gorenflo, V. K. Le and D. D. Trong, “Moment Theory and Some Inverse Problems in Heat Conduction,” Springer Verlag, Hiedelberg, 2002.
[5] S. Saha, “Estimation of Point Vibration Loads for Industrial Piping,” Journal of Pressure Vessel Technology, Vol. 131, No. 3, 2009, Article ID: 031205, 7 p.
[6] W. A. Moussa and A. N. Abdel Hamid, “On the Evaluation of Dynamic Stresses in Pipelines Using Limited Vibration Measurements and FEA in the Time Domain,” Journal of Pressure Vessel Technology, Vol. 121, No. 1, 1999, pp. 241-245. doi:10.1115/1.2883665
[7] W. A. Moussa and A. N. Abdel Hamid, “On the Evaluation of Dynamic Stresses in Pipelines Using Limited Vibration Measurements and FEA in the Frequency Domain,” Journal of Pressure Vessel Technology, Vol. 121, No. 1, 1999, pp. 37-41.
[8] S. Saha, “A Technique for Estimation of Dynamic Stresses from Field Measurements for Operating Piping,” Proceedings for International Conference in Creep and Fatigue(CF-6), Kalpakkam, 22-25 January 2012, pp. 726733.
[9] B. J. Dobson and E. Rider, “A Review of the Indirect Calculation of Excitation Forces from Measured Structural Response Data,” Journal of Mechanical Engineering Science, Vol. 204, No. 2, 1990, pp. 69-75.
[10] H. Goyder, “Method and Applications of Structural Modelling from Measured Structural Frequency Response Data,” Journal of Sound & Vibration, Vol. 68, No. 2, 1980, pp. 209-230. doi:10.1016/0022-460X(80)90466-6
[11] S. Nicaise and O. Zair, “Determination of Point Sources in Vibrating Beams by Boundary Measurements: Identifiability, Stability and Reconstruction Results,” Electronic Journal of Differential Equations, Vol. 2004, No. 20, 2004, pp. 1-17.
[12] G. Bruckner and M. Yamamoto, “Determination of Point Wave Sources by Point-Wise Observations: Stability and Reconstruction,” Inverse Problems, Vol. 16, No. 3, 2000, pp. 723-748. doi:10.1088/0266-5611/16/3/312
[13] M. Yamamoto, “Stability, Reconstruction Formula and Regularization for an Inverse Source Hyperbolic Problem by a Control Method,” Inverse Problems, Vol. 11, No. 2, 1995, pp. 481-496. doi:10.1088/0266-5611/11/2/013
[14] M. Yamamoto, “Determination of Forces in Vibrating Beams and Plates by Point-Wise and Line Observations by a Control Method,” Journal of Inverse and Ill-Posed Problems, Vol. 4, No. 5, pp. 437-457.
[15] J. C. Wachel, “Piping Vibration and Stress,” Proceedings of Machinery Vibration Monitoring & Analysis, Vibration Institute, New Orleans, 1981, pp. 1-20.
[16] OM, “Code for Operation and Maintenance of Nuclear Power Plants,” ASME, New York, 2004.
[17] L. Meirovitch, “Methods of Analytical Dynamics,” Dover Publications, New York, 2003.
[18] R. R. Craig Jr., “Structural Dynamics,” John Wiley, Hoboken, 1981.
[19] E. Kreyszig, “Introductory Functional Analysis with Applications,” John Wiley, Hoboken, 1978.
[20] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, “Numerical Recipes in C++,” Cambridge University Press, Cambridge, 2002.
[21] S. D. Downing and D. F. Socie, “Simple Rainflow Counting Algorithms,” International Journal of Fatigue, Vol. 4, No. 1, 1982, pp. 31-40.

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