Determination of the survival probability of a launch vehicle risingthrough a random wind field.

In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillators endowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the stochastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscillator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related to the corresponding linear oscillator with integer-order derivatives, is used as orthogonal basis for this scheme. Applications to the standard viscous linear and to nonlinear (Van der Pol and Duffing) oscillators are presented. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed approximate analytical solution.

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Economic considerations of the determination of investments for launch vehicle costs in the next two decades (1980–2000)

Acta Astronautica ◽

10.1016/0094-5765(81)90117-x ◽

1981 ◽

Vol 8 (11-12) ◽

pp. 1175-1194

Author(s):

Klaus P. Heiss

Keyword(s):

Launch Vehicle ◽

Economic Considerations

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Approximate survival probability determination of hysteretic systems with fractional derivative elements

Probabilistic Engineering Mechanics ◽

10.1016/j.probengmech.2017.10.001 ◽

2018 ◽

Vol 54 ◽

pp. 138-146 ◽

Cited By ~ 13

Author(s):

A. Di Matteo ◽

P.D. Spanos ◽

A. Pirrotta

Keyword(s):

Fractional Derivative ◽

Survival Probability ◽

Hysteretic Systems

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A computational method for the determination of launch vehicle trajectory dispersions

10.2514/6.1966-483 ◽

1966 ◽

Author(s):

T. MOCH

Keyword(s):

Launch Vehicle ◽

Computational Method ◽

Vehicle Trajectory

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Perpendicular-to-Grain Strength of Douglas-Fir

Canadian Journal of Civil Engineering ◽

10.1139/l75-005 ◽

1975 ◽

Vol 2 (1) ◽

pp. 50-57 ◽

Cited By ~ 16

Author(s):

J. D. Barrett ◽

R. O. Foschi ◽

S. P. Fox

Keyword(s):

Experimental Data ◽

Brittle Fracture ◽

Survival Probability ◽

Douglas Fir ◽

Curved Beams ◽

Allowable Stresses ◽

Laminated Material

Weibull's theory of brittle fracture is applied to the determination of strength of Douglas-fir wood in tension perpendicular to the grain. Results from tests on blocks of glued-laminated material uniformly stressed in tension are used to derive ultimate stresses, at a given survival probability, for pitched-tapered beams, curved beams, and griplam nail connections. The results of the theory are shown to be in agreement with experimental data. Allowable stresses are derived for blocks, pitched-tapered beams, curved beams, and the particular nailed connection studied.

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