The response probability density functions of nonlinear oscillators subjected to random excitations.

摘要

This thesis investigates the response probability density function (pdf) of general cubic nonlinear oscillators. The random excitation can be either broad band or narrow band.; The first part of this work concerns non-stationary response to a broad band excitation. Non-Gaussian closure is extended to this case and is the main approach throughout this part of the thesis. Many applications are made to cubic nonlinear oscillators. It is shown that the response pdfs of strongly nonlinear systems may have totally different pdfs for the displacement and velocity responses. The accuracy of the approach is illustrated by comparison with exact solutions or results from other approximate techniques.; The second part of this thesis considers the stationary response pdf to a narrow band random excitation. The stochastic averaging approach is utilized to yield the equations of response amplitudes. Approximate response pdfs are obtained by either equivalent nonlinearization or detailed balance for different cases. It is found that multiple maxima in the response pdf can occur for Duffing oscillators with very narrow band input. The effect of excitation bandwidth is also included in the analysis. Numerical simulations are used to verify the trend of the response pdf predicted by the theoretical results.; Although general cubic nonlinear systems are concerned in the entire thesis, more extensive studies are focused on Duffing and van der Pol oscillators, due to their importance in both theoretical research and engineering applications.