... white noises) is proposed. A one-dimensional averaged generalized Fokker–Planck–Kolmogorov equation for the transition probability density of the Hamiltonian is derived and the probability density of the stationary response of the system is obtained by using the perturbation method. Two examples, two...

...H. T. Zhu; G. K. Er; V. P. Iu; K. P. Kou The stationary probability density function (PDF) solution of the stochastic responses is derived for nonlinear oscillators subjected to both additive and multiplicative Poisson white noises. The PDF solution is governed by the generalized Fokker–Planck...

... and/or yield limits and (2) a polycrystal made of randomly oriented anisotropic grains. In each case, the spatial assignment of material randomness is a nonfractal strict-white-noise field on a 256 × 256 square lattice of homogeneous square-shaped grains; the flow rule in each grain follows associated...

...Y. Wu; W. Q. Zhu The stationary response of multi-degree-of-freedom dissipated Hamiltonian systems to random pulse trains is studied. The random pulse trains are modeled as Poisson white noises. The approximate stationary probability density function and mean-square value for the response of MDOF...

...P. D. Spanos; A. Sofi; M. Di Paola The nonstationary random response of a class of lightly damped nonlinear oscillators subjected to Gaussian white noise is considered. An approximate analytical method for determining the response envelope statistics is presented. Within the framework of stochastic...

... ) is white noise with spectral intensity S f 0 = 0.02 N 2 s and the base acceleration is taken to be the 1940 El-Centro earthquake record in the N-S direction. The parameters θ ̃ = [ k ̃ , c ̃ , σ ̃ η f , σ ̃ η z ] T used to generate...

... after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 03 January 2004 17 September 2004 15 03 2005 Monte Carlo methods Lyapunov methods stochastic systems white noise stability Stochastic differential equations are encountered...

...Giovanni Falsone In this paper some properties of the stochastic linearization method applied to nonlinear systems excited by parametric Gaussian white noises are discussed. In particular, it is shown that the linearized quantities, obtained by the author in another paper by linearizing...

... densities. In contrast, the derivation presented herein is exact, without restrictions beyond those for stochastic stability of the system. Of course, this exact solution is valid only if the excitations are modeled as white noises, so that the SDE calculus is applicable. To solve this problem...

... of a nonlocal memory hysteretic constitutive model. A nonlinear algebraic covariance equation is formulated for the single-degree-of-freedom Preisach hysteretic system subjected to stationary Gaussian white noise excitation, from which the stationary mean square response of the system is obtained...