Abstract
The history of the mathematical theory of random vibration started in 1905 with the publication by Einstein of his paper, “On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular Kinetic Theory of Heat.” He developed an approach to random vibration that is no longer widely used, but he showed the potential for mathematical treatment of random vibration. Many others joined the effort to develop methods for random vibration analysis. In 1930 Weiner formally defined spectral density, and in so doing, opened the way for the current approach to random vibration analysis. In 1958 Crandall organized a workshop at MIT to introduce the theory and practice of random vibration to engineers. The historical work of these researchers, and many others, is discussed in this paper.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ang, A., Tang, W., (1975), Probability Concepts in Engineering Planning and Design, Volume 1 – Basic Principles, John Wiley and Sons, New York.
Augusti, G., Baratta, A., and Casciati, F., (1984), Probability Methods in Structural Engineering, Chapman and Hall, New York.
Bendat, J., Piersol, A., (2000), Random Data: Analysis and Measurement Procedures, 3rd Ed., Wiley-Interscience, New York.
Blackman, R. B., Tukey, J. W., (1958), “Measurements of Power Spectra from the Viewpoint of Communication Engineering,” Bell Syst. Tech. Journ., Jan.-March.
Bolotin, V., (1984), Random Vibration of Elastic Systems, Martinus Nijhoff, The Hague, The Netherlands.
Carson, J. R., (1925), “Selective Circuits and Static Interference,” Bell System Technical Journal, pp. 265-279.
Carson, J. R., (1931), “The Statistical Energy-Frequency Spectrum of Random Disturbances,” Bell System Technical Journal, pp. 374-381.
Crandall, S., (Ed.), (1958), Random Vibration, Technology Press of MIT and John Wiley and Sons, New York.
Crandall, S., (1958a), “Mechanical Vibrations with Deterministic Excitations,” Chapter 1 in Random Vibration, S. Crandall, Ed. (1958).
Crandall, S., (1958b), “Statistical Properties of Response to Random Vibration,” Chapter 4 in Random Vibration, S. Crandall, Ed. (1958).
Crandall, S., (Ed.), (1963), Random Vibration, MIT Press, Cambridge, MA.
Crandall, S., Mark, W., (1963), Random Vibration in Mechanical Systems, Academic, New York.
Davenport, W. B., Root, W. L., (1956), Random Signals and Noise, McGraw-Hill Book Co., NY.
Einstein, A., (1905), “On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular Kinetic Theory of Heat,” Annalen der Pyhsik, V. 17, p. 549. Also, reprinted in Einstein (1956).
Einstein, A., (1956), Investigations on the Theory of the Brownian Movement, Dover Publications, New York, Edited by R. Furth.
Elishakoff, I., (1983), Probabilistic Methods in the Theory of Structures, Wiley, New York.
Feller, W., (1971), An Introduction to Probability Theory and Its Applications, John Wiley and Sons, New York.
Ferebee, R., (2000), “Loads Combination Research at Marshall Space Flight Center,” Marshall Space Flight Center, Marshall Space Flight Center, Alabama, Report No. NASA/TM-2000-210331.
Fokker, A., (1913), Dissertation, Leiden.
Fung, Y., (1953), “Statistical Aspects of Dynamic Loads,” Journal of the Aeronautical Sciences, Vol. 20, pp. 317-330.
Fung, Y., (1955), “The Analysis of Dynamic Stresses in Aircraft Structures During Landing as Nonstationary Random Processes,” J. Appl. Mech., Vol. 2, pp. 449-457.
Furth, R., (1917), Ann. D. Physik, V. 53, 177.
Ghanem, R. G., Spanos, P. D., (1991), Stochastic finite Elements: A Spectral Approach, Springer-Verlag, New York.
Gnedenko, B., (1997), Theory of Probability, 6 th Ed., Gordon and Breach Science Publishers, UK.
Himelblau, H., Kern, D. L., Manning, J. E., Piersol, A. G., Rubin, S., (2001), “Dynamic Environmental Criteria,” NASA Technical Handbook, NASA-HDBK-7005.
Housner, G., (1947), “Characteristics of Strong Motion Earthquakes,” Bull. Seism. Soc. Amer., Vol. 37, pp. 19-31.
Houdijk, A., (1928), Archives Nerlandaises des Sciences Exactes et Naturelles, Series III A, 11, p. 212.
Ibrahim, R., (1985), Parametric Random Vibration, Wiley, New York.
James, H., Nichols, N., Phillips, R., (Eds.) (1947), Theory of Servomechanisms, Radiation Laboratory Series, Vol. 25, MIT, McGraw-Hill, New York.
Kac, M., (1947), “Random Walk and the Theory of Brownian Motion,” American Mathematical Monthly, V. 54, No. 7. Reprinted in Wax (1954).
Khintchine, A., (1934), “Korrelations Theorie der Stationaren Stochastischen Prozesse,” Math. Ann., 109, 604-615.
Kolmogorov, A. N., (1931), “On Analytical Methods in the Theory of Probability,” Math. Ann., Vol. 104, pp. 415-458.
Laning, J. H., Battin, R. H., (1956), Random Processes in Automatic Control, McGraw-Hill, New York.
Liepmann, H., (1952), “On the Application of Statistical Concepts to the Buffeting Problem,” Journal of the Aeronautical Sciences, Vol. 19, No. 12, p. 793, Also, An Approach to theBuffeting Problem from Turbulence Considerations, Report No. SM-13940, Douglas Aircraft Company, Inc., 1951.
Lin, Y., (1967), Probabilistic Theory of Structural Dynamics, McGraw-Hill, New York. Republished in 1976 by Krieger, Huntington, New York.
Lyon, R. H., (1956), “Response of Strings to Random Noise Fields,” The Journal of the Acoustical Society of America, V. 28, No. 3, pp. 391-398.
Miles, J. W., (1954), “On Structural Fatigue Under Random Loading,” Journal of the Aeronautical Sciences, V. 21, pp. 753-762.
NASA, (2002), “Payload Flight Equipment Requirements and Guidelines for Safety-Critical Structures,” International Space Station Program, NASA, No. SSP 52005 Revision C.
Newland, D., (1993), Random Vibrations, Spectral and Wavelet Analysis, Longman, New York.
Nigam, N., (1983), Introduction to Random Vibrations, MIT Press, Cambridge, MA.
Ornstein, L., (1919), Proc. Acad. Amst., Vol. 21, No. 96.
Ornstein, L. S., (1927), Zeits. F. Physik, 41, p. 848.
Paez, T., (2006), “The History of Random Vibrations through 1958,” Mechanical Systems and Signal Processing, V. 20, pp. 1783-1818.
Papoulis, A., (2002), Probability, Random Variables and Stochastic Processes, 4th Ed., McGraw-Hill, New York.
Phillips, R., (1947), “Statistical Properties of Time Variable Data,” Chapter 6 in James, Nichols and Phillips (1947).
Planck, M., (1927), Berl. Ber., p. 324.
Lord Rayleigh, (1889), “On the Character of the Complete Radiation at a Given Temperature,” Philosophical Magazine, V. 27, pp. 460-469.
Roberts, J., Spanos, P., (1990), Random Vibration and Statistical Linearization, Wiley, New York.
Robson, J., (1964), An Introduction to Random Vibration, Elsevier, New York.
Rona, T., (1958), “Instrumentation for Random Vibration,” Chapter 7 in Random Vibration, S. Crandall, Ed. (1958).
Schueller, G., Shinozuka, M., (1987), (Eds.), (1987), Stochastic Methods in Structural Dynamics, Martinus Nijhoff, Boston.
Schuster, A., (1894), “On Interference Phenomena,” Philosophical Magazine, V. 37, pp. 509-545.
Schuster, A., (1897), “On Lunar and Solar Periodicities of Earthquakes,” Proceedings of the Royal Society of London, V. 61, pp. 455-465.
Schuster, A., (1899), “The Periodogram of Magnetic Declination,” Camb. Phil. Trans., 18, 108.
Schuster, A., (1900), “The Periodogram of Magnetic Declination,” Trans. Camb. Phil. Soc., 107-135.
Schuster, A., (1905), “The Periodogram and Its Optical Analogy,” Proceedings of the Royal Society, V. 77, pp. 136-140.
Siebert, W. M., (1958), “The Description of Random Processes,” Chapter 2 in Random Vibration, S. Crandall, Ed. (1958).
Smallwood, D., (1982a), “Random Vibration Testing of a Single Test Item with a Multiple Input Control System,” Proceedings of the IES Annual Meeting, IES.
Smallwood, D., (1982b), “Random Vibration Control System for Testing a Single Test Item with Multiple Inputs,” Advances in Dynamic Analysis and Testing, SAE Publication SP-529, Paper No. 821482.
v. Smoluchowski, M., (1916), Phys. Zeits., 17, p. 557.
Soong, T., Grigoriu, M., (1993), Random Vibration of Mechanical and Structural Systems, Prentice-Hall, Englewood Cliffs, NJ.
Taylor, G. I., (1920), “Diffusion by Continuous Movements,” Proceedings of the London Mathematical Society, V. 20, pp. 196-212.
Thomson,W. T.,Barton, M. V.,(1957),“The Response of Mechanical Systems to Random Excitations,” Journal of Applied MechanicsV. 24, pp. 248-251.
Uhlenbeck, G., Ornstein, L., (1930), “On the Theory of the Brownian Motion,” Physical ReviewV. 36, pp. 823-841. Reprinted in Wax (1954).
Van Lear, G. A., Uhlenbeck, G. E., (1931), “The Brownian Motion of Strings and Elastic Rods,” Physical Review, V. 38, pp. 1583-1598.
Wang, M., Uhlenbeck, G., (1945), “On the Theory of Brownian Motion II,” Reviews of Modern Physics, V. 17, Nos. 2 and 3, pp. 323-342. Reprinted in Wax (1954).
Wax, N. (ed.), (1954), Selected Papers on Noise and Stochastic Processes, Dover Publications, New York.
Wiener, N., (1930), “Generalized Harmonic Analysis,” Acta Mathematica, V. 55, No. 118.
Wirsching, P., Paez, T., Ortiz, K., (1995), Random Vibrations: Theory and Practice, Wiley, New York.
Yang, C., (1986), Random Vibration of Structures, Wiley, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this paper
Cite this paper
Paez, T.L. (2011). Random Vibration – History and Overview. In: Proulx, T. (eds) Rotating Machinery, Structural Health Monitoring, Shock and Vibration, Volume 5. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9428-8_9
Download citation
DOI: https://doi.org/10.1007/978-1-4419-9428-8_9
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9427-1
Online ISBN: 978-1-4419-9428-8
eBook Packages: EngineeringEngineering (R0)