... nonlinear dynamical systems statistical distributions Markov processes Gaussian noise white noise Fokker-Planck equation Galerkin method series (mathematics) eigenvalues and eigenfunctions boundary-value problems The response of nonlinear oscillators subjected to random excitations has been...

... to give the first two statistical moments of the true response. The second property is that, in the stationary case and in the field of the parameter estimation theory, they represent the maximum likelihood estimates of the linear model quantities fitting the original nonlinear response. Gaussian noise...

... spectral analysis Gaussian noise The investigation of the maximal Lyapunov exponent for dynamical systems which are excited by stochastic processes is the primary research focus in the fields of random dynamical systems and stochastic bifurcation. This is mainly attributed to the fact...

... everywhere. classical mechanics white noise Gaussian noise 20 June 2001 25 Sept 2001 03 05 2002 Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS . Manuscript received...

... OF APPLIED MECHANICS . 18 April 2000 hysteresis stochastic processes Gaussian distribution white noise Gaussian noise Nonlinear hysteretic dampers and isolators have been widely used in the past decade. In addition, there has been an increasing interest recently in using smart...