Critical excitation for elastic-plastic structures via statistical equivalent linearization

Abstract Since earthquake ground motions and their effects on structural responses are very uncertain even with the present knowledge, it is desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new random critical excitation method for single-degree-of-freedom (SDOF) elastic–plastic structures is proposed. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. In contrast to linear elastic structures, transfer functions and related simple expressions for response evaluation cannot be defined in elastic–plastic structures and difficulties arise in describing the peak responses except elastic–plastic time-history response analysis. Statistical equivalent linearization is utilized to estimate the elastic–plastic stochastic peak responses approximately. The critical excitations are obtained for two examples and compared with the corresponding recorded earthquake ground motions.

[1]  Y. K. Wen,et al.  Methods of Random Vibration for Inelastic Structures , 1989 .

[2]  P. Spanos,et al.  Hysteretic structural vibrations under random load , 1979 .

[3]  A. J. Philippacopoulos,et al.  Seismic Inputs for Nonlinear Structures , 1984 .

[4]  Izuru Takewaki,et al.  Optimal damper placement for critical excitation , 2000 .

[5]  D. E. Hudson.  Some problems in the application of spectrum techniques to strong-motion earthquake analysis , 1962 .

[6]  C. S. Manohar,et al.  CRITICAL SEISMIC VECTOR RANDOM EXCITATIONS FOR MULTIPLY SUPPORTED STRUCTURES , 1998 .

[7]  Masanobu Shinozuka,et al.  Maximum Structural Response to Seismic Excitations , 1970 .

[8]  Vitelmo V. Bertero,et al.  Uncertainties in Establishing Design Earthquakes , 1987 .

[9]  Y. Wen.  Equivalent Linearization for Hysteretic Systems Under Random Excitation , 1980 .

[10]  Bruce D. Westermo.  The critical excitation and response of simple dynamic systems , 1985 .

[11]  Takuji Kobori,et al.  Statistical Linearization Techniques of Hysteretic Structures to Earthquake Excitations , 1973 .

[12]  R. F. Drenick,et al.  The Critical Excitation of Nonlinear Systems , 1977 .

[13]  A. Papoulis,et al.  Maximum response with input energy constraints and the matched filter principle , 1970 .

[14]  Yakov Ben-Haim,et al.  Maximum Structural Response Using Convex Models , 1996 .

[15]  R. N. Iyengar,et al.  Nonstationary Random Critical Seismic Excitations , 1987 .

[16]  P. Spanos,et al.  Random vibration and statistical linearization , 1990 .

[17]  C. S. Manohar,et al.  Critical earthquake input power spectral density function models for engineering structures , 1995 .

[18]  Chris P. Pantelides,et al.  CONVEX MODEL FOR SEISMIC DESIGN OF STRUCTURES—I: ANALYSIS , 1996 .

[19]  Masanobu Shinozuka,et al.  A generalization of the Drenick-Shinozuka model for bounds on the seismic response of a single-degree-of-freedom system , 1998 .

[20]  Rudolf F. Drenick,et al.  Model-Free Design of Aseismic Structures , 1970 .

[21]  Thomas K. Caughey,et al.  Random Excitation of a System With Bilinear Hysteresis , 1960 .

[22]  Wilfred D. Iwan,et al.  A linearization scheme for hysteretic systems subjected to random excitation , 1981 .

[23]  Ross B. Corotis,et al.  Generation of critical stochastic earthquakes , 1992 .

[24]  P. Spanos,et al.  Stochastic Linearization in Structural Dynamics , 1988 .

[25]  R. Narayana Iyengar,et al.  Worst inputs and a bound on the highest peak statistics of a class of non-linear systems , 1972 .

[26]  A. Papoulis.  Limits on bandlimited signals , 1967 .

[27]  I. Elishakoff,et al.  Convex models of uncertainty in applied mechanics , 1990 .