Approximate solution techniques for randomly excited non-linear systems

Student: Ashish Harbindu
Supervisors: Prof. Aposotolos Papageorgiou


Randomly excited non-linear dynamic systems are frequently met in engineering practice. The source of randomness may arise from earthquake ground motion or wind or wave motions at sea exciting offshore structures. The objectives are investigation and thorough understanding of stochastic nonlinear phenomena as well computation of certain non-linear response characteristics.

The excitations, that will be studied, are stationary Gaussian processes. These processes can be white noise processes or processes with band limited frequency spectra. Both models for stationary and nonstationary have been discussed with a short description of power spectral density (PSD) function for random processes.

The primary motive of this study to present thorough investigation of approximate techniques for estimating the stationary probability density function (PDF) of the response of nonlinear system subjected to additive Gaussian white noise excitations. Attention is focused on the exponential closure method in which the probability density function can be approximated with the exponential function of polynomial in state variables. Special measure is taken to satisfy Fokker-Planck-Kolmogorov (FPK) equation in the weak sense of integration with the assumed PDF. Several nonlinear oscillators are under additive white noises were solved. Method is also extended for higher order of assumed PDF.

The response obtained from numerical results showed close approximation with exact PDF regardless of degree of system non-linearity. Higher order assumed PDF coincide with exact ones regardless of degree of non-linearity in the system.

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