Tail-equivalent linearization method for nonlinear random vibration

Atalik, 1976, Stochastic linearization of multi-degree of freedom nonlinear systems, Earthquake Engineering and Structural Dynamics, 4, 411, 10.1002/eqe.4290040408 Au, 2001, First excursion probability for linear systems by very efficient algorithm, Probabilistic Engineering Mechanics, 16, 193, 10.1016/S0266-8920(01)00002-9 Bouc, 1963, Forced vibration of mechanical systems with hysteresis, 315 Casciati, 1993, A new philosophy for stochastic equivalent linearization, Probabilistic Engineering Mechanics, 8, 179, 10.1016/0266-8920(93)90013-L Caughey, 1963, Equivalent linearization techniques, Journal of the Acoustical Society of America, 35, 1706, 10.1121/1.1918794 Der Kiureghian, 1998, Multiple design points in first and second-order reliability, Structural Safety, 20, 37, 10.1016/S0167-4730(97)00026-X Der Kiureghian, 2000, The geometry of random vibrations and solutions by FORM and SORM, Probabilistic Engineering Mechanics, 15, 81, 10.1016/S0266-8920(99)00011-9 Ditlevsen, 1996 Elishakoff, 1992, Comparison of new stochastic linearization criteria, 201 Hagen, 1991, Vector process out-crossing as parallel system sensitivity measure, Journal of Engineering Mechanics, ASCE, 117, 2201, 10.1061/(ASCE)0733-9399(1991)117:10(2201) Haukaas, 2005, Parameter sensitivity and importance measures in nonlinear finite element reliability analysis, Journal of Engineering Mechanics, ASCE, 131, 1013, 10.1061/(ASCE)0733-9399(2005)131:10(1013) Haukaas, 2006, Strategies for finding the design point in nonlinear finite element reliability analysis, Probabilistic Engineering Mechanics, 21, 133, 10.1016/j.probengmech.2005.07.005 Kanai, 1957, Semi-empirical formula for the seismic characterization of the ground, Bulletin of the Earthquake Research Institute, University of Tokyo, 35, 309 Kleiber, 1997 Koo, 2005, Design point excitation for nonlinear random vibration, Probabilistic Engineering Mechanics, 20, 136, 10.1016/j.probengmech.2005.04.001 Li C-C, Der Kiureghian A. Mean out-crossing rate of nonlinear response to stochastic input. In: Lemaire M, Favre J-L, Mbarki A, editors. Proceedings of 7th international conference on applications of statistics and probability in civil engineering reliability and risk analysis, 1995. p. 295–302 Lin, 2004 Liu, 1991, Optimization algorithms for structural reliability, Structural Safety, 9, 161, 10.1016/0167-4730(91)90041-7 Lutes, 2004 Roberts, 1990 Shinozuka, 1972, Monte Carlo solution of structural dynamics, Computers and Structures, 2, 855, 10.1016/0045-7949(72)90043-0 Soong, 1993 Tajimi H. A statistical method of determining the maximum response of a building structure during an earthquake. In: Proceedings of the 2nd world conference on earthquake engineering. 1960. p. 781–97 Vamvatsikos, 2002, Incremental dynamic analysis, Earthquake Engineering and Structural Dynamics, 31, 491, 10.1002/eqe.141 Vanmarcke, 1975, On the distribution of the first-passage time for normal stationary random processes, Journal of Applied Mechanics, ASME, 42, 215, 10.1115/1.3423521 Wen, 1976, Method for random vibration of hysteretic systems, Journal of Engineering Mechanics Division, ASCE, 102, 249, 10.1061/JMCEA3.0002106 Wen, 1980, Equivalent linearization for hysteretic systems under random excitation, Journal of Applied Mechanics, ASME, 47, 150, 10.1115/1.3153594 Zhang, 1993, Dynamic response sensitivity of inelastic structures, Computer Methods in Applied Mechanics and Engineering, 108, 23, 10.1016/0045-7825(93)90151-M