Random Vibration of Rotating Machines under Earthquake Excitations
Publication: Journal of Engineering Mechanics
Volume 112, Issue 6
Abstract
Random vibration of rotating machines subjected to seismic excitations is analyzed in which the six‐component earthquake ground motions are modeled as nonstationary random processes. The six‐component earthquake inputs including the rotational components of base excitations, result in not only nonhomogeneous excitations but also parametric excitations. Thus, the classical spectral analysis of random vibration is not applicable. Furthermore, both nonhomogeneous and parametric random excitations are correlated random processes, making the problem even more difficult to solve analytically. To date random vibration of such a complicated problem has not been investigated. The method of Monte Carlo simulation is used to simulate the six‐component nonstationary earthquake ground motions and to determine the statistics of the response of rotating machines. The significance of seismic base rotations on the overall structural response is examined. A numerical example is worked out to demonstrate the methodology employed.
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References
1.
Ang, A. H.‐S., “Probability Concepts in Earthquake Engineering,” Applied Mechanics in Earthquake Engineering, W. D. Iwan (Ed.), ASME, AMD Vol. 8, New York, N.Y., 1974.
2.
Ang, A. H.‐S., and Shinozuka, M., “Probabilistic Mechanics and Structural Reliability,” Proc. ASCE Conference, Tucson, Ariz., Jan. 10–12, 1979.
3.
Asmis, G. J. K., and Duff, C. G., “Seismic Design of Gyroscopic Systems,” ASME Paper 78‐PVP‐44, ASME/CSME Pressure Vessels and Piping Conference, Montreal, Canada, 1978.
4.
Asmis, G. J. K., “Response of Rotating Machinery Subjected to Seismic Excitation,” Eng. Des. Earthquake Environ., IMechE Conf. Publ., Dec., 1978, London, U.K., pp. 215–225.
5.
Ghafori‐Ashtiani, M., and Singh, M. P., “Seismic Response for Multi‐Component Earthquakes,” Technical Report No. VPI‐E‐84‐17, Dept. of Engineering Science and Mechanics, VPI and State Univ., Blacksburg, Va., Apr., 1984.
6.
Goldstein, H. H., Classical Mechanics, 2nd ed., Addison‐Wesley Reading, 1980.
7.
Gupta, K. K., “Free Vibration Analysis of Spinning Structural Systems,” International Journal for Numerical Methods in Engineering, No. 5, 1973, pp. 395–418.
8.
Hart, G. C., Dijuoio, R. M., Jr., and Lew, M., “Torsional Response of High‐Rise Buildings,” Journal of the Structural Division, ASCE, Vol. 101, No. ST2, Paper 11126, Feb., 1975, pp. 397–416.
9.
Iwatsubo, T., Kawahara, I., Nakagawa, N., and Kawai, R., “Reliability Design of Rotating Machine Against Earthquake Excitation,” Bulletin ASME, Vol. 22, No. 173, Nov., 1979, pp. 1632–1639.
10.
Iyengar, R. N., and Shinozuka, M., “Effect of Self‐Weight and Vertical Acceleration on the Behavior of Tall Structures During Earthquake,” International Journal of Earthquake Engineering and Structural Dynamics, Vol. 1, No. 1, 1972, pp. 69–78.
11.
Kameda, H., “Stochastic Process Models of Strong Earthquake Motions for Inelastic Structural Response,” in Proc. of the U.S.‐Southeast Asia Symp. on Engineering for Natural Hazards Protection, Manila, 1977, A. H.‐S. Ang, Ed., Dept. of Civil Engineering, College of Engineering, Univ. of Illinois at Urbana‐Champaign, 1978.
12.
Kim, K. B., “Random Vibration of Rotating Machines Under Earthquake Excitations,” thesis presented to The George Washington University, Washington, D.C., in Jan., 1986, in partial fulfillment of the requirements for the degree of Doctor of Science.
13.
Kuz'ma, V. M., “Resonant Modes of a Gyroscope on a Randomly Vibrating Base,” Prikladnaya Mekhanika, Vol. 16, No. 9, 1980, pp. 104–109.
14.
Lin, Y. K., Probabilistic Theory of Structural Dynamics, Kreiger Publishing Company, New York, N.Y., 1976.
15.
Liu, S. C., “Evolutionary Power Spectral Density of Strong Motion Earthquake,” Bulletin Seismological Society of America, Vol. 60, No. 3, 1970, pp. 891–900.
16.
Liu, S. C., et al., “Optimal Aseismic Design of Building and Equipment,” Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EM3, June, 1976, pp. 395–414.
17.
Lund, J. W., “Modal Response of a Flexible Rotor in Fluid‐Film Bearing,” Journal of Engineering for Industry, Trans. ASME, No. 96, 1974, pp. 525–533.
18.
Lund, J. W., “Response Characteristics of a Rotor With Flexible, Damped Supports,” Symp. Dyn. Rotors, IUTAM, Lyngby, Denmark, Springer‐Verlag, 1975, pp. 319–349.
19.
Lund, J. W., and Thomsen, K. K., “A Calculation Method and Data for the Dynamic Coefficients of Oil‐Lubricated Journal Bearings,” Topics Fluid Film Bearing Syst. Des. Optimization, ASME Conference, Chicago, 1978, pp. 1–28.
20.
Lund, J. W., “Evaluation of Stiffness and Damping Coefficients for Fluid‐Film Bearings,” Shock and Vibration Digest, Vol. 11, No. 1, 1979, pp. 5–10.
21.
Meirovitch, L., Methods of Analytical Dynamics, McGraw‐Hill, New York, N.Y., 1970.
22.
Nakagawa, E., Suita, T., and Azuma, T., “Earthquake Response Analysis of a Flexible Rotor Supported in Fluid‐Film Bearings,” Ishikawajima‐Harima Engineering Review, Vol. 18, No. 1, 1978, pp. 1–5.
23.
Newland, D. E., An Introduction to Random Vibration and Spectral Analysis, Longman Publishing Company, London, U.K., New York, N.Y., 1975.
24.
Newmark, N. M., “A Method of Computation for Structural Dynamics,” Journal of the Engineering Mechanics Division, ASCE, Vol. 85, No. EM3, July, 1959, pp. 67–94.
25.
Newmark, N. M., “Torsion in Symmetrical Building,” Proceedings of the Fourth World Conference on Earthquake Engineering, Santiago, Chile, Vol. 2, No. A.3, pp. 19–32.
26.
Penzien, J., and Watabe, M., “Characteristics of 3‐Dimensional Earthquake Ground Motions,” Earthquake Engineering and Structural Dynamics, Vol. 4, 1975, pp. 365–373.
27.
Ruddy, A. V., and Smith, D. S., “An Introduction to the Influence of the Bearings on the Dynamics of Rotating Machinery,” Tribology International, Vol. 13, 1980, pp. 199–203.
28.
Shimogo, T., Aida, T., and Nakano, M., “Seismic Response of a Flexible Rotor,” Proc. 2nd Intl. Conf., Vib. Rotating Mach., Churchill College, Cambridge, U.K., Sept. 1–4, 1980, pp. 321–326.
29.
Shinozuka, M., and Jan, C.‐M., “Digital Simulation of Random Processes and Its Applications,” Journal of Sound and Vibration, Vol. 25, Jan., 1972, pp. 111–120.
30.
Shinozuka, M., and Yao, J. T. P. (Eds.), “Probabilistic Methods in Structural Engineering,” Proc. ASCE Conference, St. Louis, Mo., Oct. 26–27, 1981.
31.
Smith, C. B., “Seismic and Operational Vibration Problems in Nuclear Power Plants,” Shock and Vibration Digest, Vol. 8, No. 11, 1976, pp. 3–13.
32.
Soni, A. H., and Srinivasan, V., “Seismic Analysis of a Gyroscopic Mechanical System,” J. Vib., Stress Reliability Des., Trans. ASME, Vol. 105, 1983, pp. 449–455.
33.
Soni, A. H., and Srinivasan, V., “Seismic Analysis of a Rotor‐Bearing System,” Journal of Earthquake Engineering and Structural Dynamics, Vol. 12, 1984, pp. 287–311.
34.
Srinivasan, V., and Soni, A. H., “Seismic Analysis of Rotating Mechanical Systems—A Review,” The Shock and Vibration Digest, Vol. 14, No. 6, 1982, pp. 13–19.
35.
Tessarzik, J. M., Chiang, T., and Badgley, R. N., “The Response of Rotating Machinery to External Random Vibration,” Journal of Engineering for Industry, Trans. ASME, Vol. 96, No. 2, May, 1974, pp. 477–489.
36.
Timoshenko, S. P., “On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars,” Phil. Mag., Vol. 41, 1921, pp. 744–746.
37.
Villasor, A. P., “Seismic Analysis of a Reactor Coolant Pump by the Response Spectrum Method,” Nuclear Eng. Des., Vol. 38, 1976, pp. 527–542.
38.
Yang, J. N., “Simulation of Random Envelope Processes,” Journal of Sound and Vibration, Vol. 21, No. 1, 1973, pp. 73–85.
39.
Yang, J. N., Lin, Y. K., and Sae‐Ung, S., “Tall Building Response to Earthquake Excitations,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM4, Aug., 1980, pp. 801–817.
40.
Yang, J. N., Sae‐Ung, S., and Lin, Y. K., “Variability of Tall Building Response to Earthquake with Changing Epicenter Direction,” Earthquake Engineering and Structural Dynamics, Vol. 10, 1982, pp. 211–223.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 112 • Issue 6 • June 1986
Pages: 550 - 565
Copyright
Copyright © 1986 ASCE.
History
Published online: Jun 1, 1986
Published in print: Jun 1986
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