Badrakhan, Farouk Rational study of hysteretic systems under stationary random excitation. (English) Zbl 0614.73094 Int. J. Non-Linear Mech. 22, 315-325 (1987). The ”trace” method together with a new definition of the normalization factor of the response distribution density related to a probable maximum peak value of the response, lead to quasi-deterministic results which seem to be more realistic and more rational than those given by other known methods. In the particular case of bilinear hysteresis, it is shown that the statistical properties obtained are bounded by those of two limit linear cases. MSC: 74H50 Random vibrations in dynamical problems in solid mechanics 70L05 Random vibrations in mechanics of particles and systems Keywords:Gaussian distributions; Rayleigh distributions; Monte Carlo simulation; normalization factor; response distribution density; probable maximum peak value of the response; quasi-deterministic results; bilinear hysteresis PDFBibTeX XMLCite \textit{F. Badrakhan}, Int. J. Non-Linear Mech. 22, 315--325 (1987; Zbl 0614.73094) Full Text: DOI