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  • 1
    ISSN: 1573-269X
    Keywords: stochastic bifurcation ; Lyapunov exponents ; Fokker-Planck equations ; Monte-Carlo simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract At the state of statistical stationarity, the response of a nonlinear system under multiplicative random excitations can be either trivial or non-trivial, depending on the spectral levels of the excitations and the values of certain system parameters. Assuming that the random excitations are Gaussian white noises, the two types of response may be investigated by way of their stationary densities, which are obtainable for first order dynamical systems and for higher order dynamical systems belonging to the class of generalized stationary potential. Alternatively, the Lyapunov exponents can be computed for perturbation from either the trivial or non-trivial solution, since a negative sign for the greatest Lyapunov exponent provides both the necessary and sufficient conditions for the stability of sample functions with probability one. It is shown in two specific examples, that the boundary at which the greatest Lyapunov exponent changes its sign coincides with the boundary for regularity (or being normalizable) for the probability density in both the trivial and non-trivial solutions. Thus, the stability conditions in the strong sense of probability one and the weak sense in distribution are identical in these cases.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2019-06-28
    Description: This report supplements a previous report of the same title submitted in June, 1992. It summarizes additional analytical techniques which have been developed for predicting the response of linear and nonlinear structures to noise excitations generated by large propulsion power plants. The report is divided into nine chapters. The first two deal with incomplete knowledge of boundary conditions of engineering structures. The incomplete knowledge is characterized by a convex set, and its diagnosis is formulated as a multi-hypothesis discrete decision-making algorithm with attendant criteria of adaptive termination.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-196447 , NAS 1.26:196447
    Format: application/pdf
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