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  • 1
    Electronic Resource
    Electronic Resource
    Necessary and sufficient conditions for existence of stationary solutions of some nonlinear stochastic systems (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 75-90 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01857586
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    Paper (German National Licenses)
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  • 2
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    Analytical procedures for estimating structural response to acoustic fields generated by advanced launch systems, phase 2 (1994)
    In:  CASI
    Details
    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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    NASA TECHNICAL REPORTS
  • 3
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    Response of periodic beam to supersonic boundary-layer pressure fluctuations (1977)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: The response of a periodic beam (modeling a periodic fuselage) to supersonic boundary-layer pressure fluctuations is analyzed on the basis of a scheme in which a decaying turbulence is treated as a superposition of frozen-pattern components, thus allowing the structural response to be similarly superposed and the advantage of frozen-pattern analysis to be maximally utilized. The fundamental solution required for the construction of the total response is one corresponding to the excitation of a frozen-pattern sinusoid. To obtain this fundamental solution, the formulation follows Mead's wave-propagation method (1971), but also takes into account the effect of freestream velocity on the same side of the turbulence excitation and the effect of a cavity on the opposite side of the excitation. As a numerical example, the spectral density of the structural response is computed and the results are compared with experimental data.
    Keywords: STRUCTURAL MECHANICS
    Type: Symposium on Stochastic problems in dynamics; Jul 19, 1976 - Jul 23, 1976; Southampton
    Format: text
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    NASA TECHNICAL REPORTS
  • 4
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    Vibroacoustic response of structures and perturbation Reynolds stress near structure-turbulence interface (1977)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: The interaction between a turbulent flow and certain types of structures which respond to its excitation is investigated. One-dimensional models were used to develop the basic ideas applied to a second model resembling the fuselage construction of an aircraft. In the two-dimensional case a simple membrane, with a small random variation in the membrane tension, was used. A decaying turbulence was constructed by superposing infinitely many components, each of which is convected as a frozen pattern at a different velocity. Structure-turbulence interaction results are presented in terms of the spectral densities of the structural response and the perturbation Reynolds stress in the fluid at the vicinity of the interface.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-CR-2876
    Format: application/pdf
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