Plastic Input Motion: Transformation for the Response of Yielding Oscillators
Publication: Journal of Engineering Mechanics
Volume 138, Issue 7
Abstract
A transformation method is presented for the response of yielding oscillators to dynamic loading. The method employs a translation in the ordinates and the abscissa of the excitation function by means of a pair of parameters uniquely dependent on the yielding resistance and the vibrational characteristics of the system. By this approach: (1) the differential operator becomes linearlike, with the nonlinearity transferred to the right-hand side; (2) the initial conditions are simplified; and (3) the modified forcing term becomes uniquely associated with the development of plastic deformation. The theory is applied to various yielding oscillators subjected to idealized earthquake pulses, with the modified excitation function termed plastic input motion (PIM). A procedure for applying the method to general waveforms is provided. The coordinates of PIM may be discontinuous and significantly smaller than those of the original excitation function, as a considerable amount of ground acceleration is devoted to overcoming the elastic resistance of the system. The theory can be useful in earthquake engineering by offering a replacement to physical ground motions with system-dependent PIMs for establishing demand indices.
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Acknowledgments
The research at hand was supported by NTUA Basic Research Program Grant No. 65/1720. The writers are grateful for this support. The valuable comments of two anonymous reviewers helped with improving the quality of the paper.
References
Barenblatt, G. I. (1996). Scaling, self-similarity and intermediate asymptotics, Cambridge Univ. Press, Cambridge, U.K.
Bathe, K.-J., and Gracewski, S. (1981). “On nonlinear dynamic analysis using substructuring and mode superposition.” Comput. Struct., 13(5–6), 699–707.CMSTCJ
Biggs, J. M. (1964). Introduction to structural dynamics, McGraw-Hill, New York.
Bracewell, R. N. (1986). The Fourier transform and its applications, 2nd Ed., Chapter 14, McGraw-Hill, New York, 392–396.
Bray, J. D., and Rodriguez-Marek, A. (2004). “Characterization of forward-directivity ground motions in the near-fault region.” Soil Dyn. Earthquake Eng., 24(11), 815–828.IJDEDD
Chopra, A. K. (2006). Dynamics of structures, Prentice-Hall, Upper Saddle River, NJ.
Cuesta, I., and Aschheim, M. A. (2001). “Isoductile strengths and strength reduction factors of elasto-plastic SDOF systems subjected to simple waveforms.” Earthquake Eng. Struct. Dyn., 30(7), 1043–1059.IJEEBG
Kramer, S. L. (1996). Geotechnical earthquake engineering, Prentice Hall, Upper Saddle River, NJ.
Makris, N., and Black, C. J. (2004). “Dimensional analysis of bilinear oscillators under pulse-type excitations.” J. Eng. Mech.JENMDT, 130(9), 1019–1031.
Miranda, E., and Bertero, V. (1994). “Evaluation of strength reduction factors of earthquake-resistant design.” Earthquake Spectra, 10(2), 357–379.EASPEF
Mylonakis, G., and Reinhorn, A. M. (2001). “Yielding oscillator under triangular ground acceleration pulse.” J. Earthquake Eng., 5(2), 225–251.
Mylonakis, G., and Voyagaki, E. (2006). “Yielding oscillator subjected to simple pulse waveforms: Numerical analysis and closed-form solutions.” Earthquake Eng. Struct. Dyn., 35(15), 1949–1974.IJEEBG
Newmark, N. M. (1965). “Effects of earthquakes on dams and embankments.” Geotechnique, 15(2), 139–160.GTNQA8
Newmark, N. M., and Rosenblueth, E. (1971). Fundamentals of earthquake engineering, Prentice-Hall, Englewood Cliffs, NJ.
Tang, Y. C., and Zhang, J. (2011). “Response spectrum-oriented pulse identification and magnitude scaling of forward directivity pulses in near-fault ground motions.” Soil Dyn. Earthquake Eng., 31(1), 59–76.IJDEDD
Veletsos, A. S., and Newmark, N. M. (1960). “Effect of inelastic behavior on the response of simple system to earthquake motion.” Proc., 2nd World Conf. on Earthquake Engineering, Tokyo, 895–912.
Veletsos, A. S., and Ventura, C. E. (1984). “Efficient analysis of dynamic response of linear systems.” Earthquake Eng. Struct. Dyn., 12(4), 521–536.IJEEBG
Villaverde, R., and Hanna, M. M. (1992). “Efficient mode superposition algorithm for seismic analysis of non-linear structures.” Earthquake Eng. Struct. Dyn., 21(10), 849–858.IJEEBG
Voyagaki, E. (2011). “Contributions to dynamic response of yielding systems to near-fault earthquake motions.” Ph.D. thesis, School of Civil Engineering, National Technical Univ., Athens, Greece.
Voyagaki, E., Mylonakis, G., and Psycharis, I. N. (2011). “A shift approach for the dynamic response of rigid-plastic systems.” Earthquake Eng. Struct. Dyn., 40(8), 847–866.IJEEBG
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© 2012. American Society of Civil Engineers.
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Received: Aug 14, 2010
Accepted: Dec 8, 2011
Published online: Dec 12, 2011
Published in print: Jul 1, 2012
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