Associate Linear System Approach to Nonlinear Random Vibration
Publication: Journal of Engineering Mechanics
Volume 117, Issue 10
Abstract
An approach is developed for approximate random vibration analysis of multidegree hysteretic structures based on the concept of energy balance, i.e., the excitation energy is balanced with the energy the structure dissipates in hysteresis and viscous damping. All response measures are estimated based on random vibration analyses of an associate linear system. Inelastic response measures, such as cumulative plastic drift at the local level, are modeled based on Markov process theory. The approach is developed for elastoplastic and trilinear hysteretic multidegree structures. Analytical results are compared to those based on simulation for the distribution of the mean peak ductility ratio over the structure's height for several multistory buildings subjected to stochastic seismic excitation. The focus is on studying the effect of earthquake intensity and the presence of a soft story on the distribution of ductility ratio versus height. Insights gained from such analyses should be helpful in evaluating seismic design strategies of buildings.
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References
1.
Baber, T. T., and Wen, Y. K. (1981). “Random vibration of hysteretic degrading systems.” J. Engrg. Mech., ASCE, 107(6).
2.
Caughey, T. K. (1971). “Nonlinear theory of random vibrations.” Adv. Appl. Mech., 11, 209–253.
3.
Çinlar, E. (1975a). Introduction to stochastic processes. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
4.
Çiniar, E. (1975b). “Lévy systems of Markov additive processes.” Z. Wahrscheinlichkeitstheorie verw. Ger., 31, 175–185.
5.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures. McGraw‐Hill, Inc., New York, N.Y.
6.
Crandall, S. H., Khabbaz, G. R., and Manning, J. E. (1964). “Random vibration of an oscillator with nonlinear damping.” J. Acoust. Soc. Amer., 36(7), 1330–1334.
7.
Gazetas, G. (1976). “Random vibration analysis of inelastic multi‐degree‐of‐freedom systems subjected to earthquake ground motions.” Research Report R76‐39, Massachusetts Inst. of Tech., Cambridge, Mass.
8.
Grossmayer, R. (1981). “Stochastic analysis of elasto‐plastic systems.” J. Engrg. Mech. Div., ASCE, 39, 97–115.
9.
Grossmayer, R., and Iwan, W. D. (1981). “A linearization scheme for hysteretic system subjected to random excitation.” Earthquake Engrg. Struct. Dyn., 9, 171–185.
10.
Hughes, T. (1987). The finite element method. Prentice‐Hall, Englewood Cliffs, N.J.
11.
Irschik, H. (1986). “Nonstationary random vibration of yielding multi‐degree‐offreedom systems: Method of effective envelope functions.” Acta Mechanica, 60, 265–280.
12.
Karnopp, D. (1967). “Power balance method for nonlinear random vibration.” J. Appl. Mech., 34(1), 212–214.
13.
Karnopp, D., and Scharton, T. D. (1966). “Plastic deformation in random vibration.” J. Acoust. Soc. Am., 39, 1154–1161.
14.
Lai, S. P. (1980). “Overall safety assessment of multistory steel buildings subjected to earthquake loads.” Research Report R80‐26, Massachusetts Inst. of Tech., Cambridge, Mass.
15.
Ricks, D. C. (1983). “Important statistics of hysteretic random vibration.” thesis presented to Massachusetts Inst. of Tech. at Cambridge, Mass., at Cambridge, Mass., in partial fulfillment of the requirement for the degree of Master of Sciences.
16.
Roberts, J. B. (1981a). “Response of nonlinear mechanical systems to random/ excitation; Part I: Markov methods.” Shock Vibration Digest, 13(4), 17–28, April, 1981.
17.
Roberts, J. B. (1981b). “Response of nonlinear mechanical systems to random excitation; Part II: Equivalent linearization and other methods,” Shock Vib. Dig., 13(5), 15–29.
18.
Roberts, J. B. (1986). “First‐passage probabilities for randomly excited systems: Difffusion methods.” Probabil. Engrg. Mech., 1(2).
19.
Spencer, B. F. (1986). Reliability of randomly excited hysteretic structures. Springer‐Verlag.
20.
Suzuki, Y. (1985). Seismic reliability analysis of hysteretic structures based on stochastic differential equations. Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan.
21.
Vanmarcke, E. H. (1976). “Structural response to earthquakes.” Seismic risk and engineering decisions, C. Lomnitz, and E. Rosenblueth, eds., Elsevier, Amsterdam, the Netherlands.
22.
Vanmarcke, E. H. (1987). “Spatial averaging of earthquake ground motion: The effect on response spectra.” Proc. EPRI Workshop on Engineering Characterization of Small‐Magnitude Earthquakes.
23.
Vanmarcke, E. H., and Veneziano, D. (1973). “Probabilistic seismic response of simple inelastic systems.” Proc. 5th WCEE, 2.
24.
Wen, Y. K. (1980). “Equivalent linearization for hysteretic systems under random excitation.” J. Appl. Mech., ASME, 47(1), 150–154.
25.
Yanev, P. I. (1970). “Response of simple inelastic systems to random excitation.” Thesis presented to Massachusetts Inst. of Tech., at Cambridge Mass., in partial fulfillment of the requirement for the degree of Master of Science.
26.
Ziegler, F., and Irschik, H. (1985). “Nonstationary random vibrations of yielding beams.” Proc. 8th Int. SMirt Conf.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 117 • Issue 10 • October 1991
Pages: 2407 - 2428
Copyright
Copyright © 1991 ASCE.
History
Published online: Oct 1, 1991
Published in print: Oct 1991
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