Non-Gaussian probability density function of SDOF linear structures under wind actions

Abstract Wind velocity is usually analytically described adding a static mean term to a zero mean fluctuation stationary process. The corresponding aerodynamic alongwind force acting on a single degree of freedom (SDOF) structure can be considered as a sum of three terms proportional to the mean wind velocity, to the product between mean and fluctuating part of the wind velocity and to the square power of the fluctuating wind velocity, respectively. The latter term, often neglected in the literature, is responsible for the non-Gaussian behaviour of the response. In this paper a method for the evaluation of the stationary probability density function of SDOF structures subjected to non-Gauss…

A method for the probabilistic analysis of nonlinear systems

Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…

Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process

In this paper the exact stationary solution in terms of probability density function for a restricted class of non-linear systems under both external and parametric non-normal delta-correlated processes is presented. This class has been obtained by imposing a given probability distribution and finding the corresponding dynamical system which satisfies the modified Fokker-Planck equation. The effectiveness of the results has been verified by means of a Monte Carlo simulation.

Extended Entropy Functional for Nonlinear Systems in Stochastic Dynamics

Stationary and Nontationary Response Probability Density Function of a Beam under Poisson White Noise

In this paper an approximate explicit probability density function for the analysis of external oscillations of a linear and geometric nonlinear simply supported beam driven by random pulses is proposed. The adopted impulsive loading model is the Poisson White Noise , that is a process having Dirac’s delta occurrences with random intensity distributed in time according to Poisson’s law. The response probability density function can be obtained solving the related Kolmogorov-Feller (KF) integro-differential equation. An approximated solution, using path integral method, is derived transforming the KF equation to a first order partial differential equation. The method of characteristic is the…

Stationary and non-stationary probability density function for non-linear oscillators

A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.

Non Linear Systems Under Complex α-Stable Le´vy White Noise

The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME

Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses

Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.