Abstract
We turn now to the investigation of differential equations whose coefficients are random functions (“parametric excitation”). Such equations occur frequently in applications: flutter of aircraft wings in turbulent atmosphere, instruments on shaking ground or shaking suspensions, wave propagation in inhomogeneous media etc. In this connection, the question of stability or instability of the motion is of fundamental importance.
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Literature
W.W. Bolotin: Kinetische Stabilität elastischer Systeme. VEB Deutscher Verlag der Wissenschaften, Berlin 1961.
F. Kozin: A survey of stability of stochastic systems. Automatica 5 (1969), 95.
F. Kozin: On almost sure stability of linear sys tems with random coefficients. J.Math.Phys. 42 (1963), 59.
E.F. Infante:On the stability of some linear non-autonomous random systems. J.Appl. Mech. 35 (1968), 7.
A.H. Gray, Jr.: Behavior of linear systems with random parametric excitation. J.Acoust.Soc.America 37 (1965), 235.
P.W.U. Graefe: On the stabilization of unstable linear systems by white noise coefficients. Ing.-Arch. 35 (1966), 276.
J.L.Bogdanoff and F.Kozin: Moments of the output of linear random systems. J.Acoust. Soc.America 34 (1962), 1063.
J.B. Keller: Stochastic equations and wave propaga tion in random media. Proc.Symposia Appl. Math., vol.XVI, 1964,p. 145.
W.E. Boyce: A “dishonest” approach to certain stochastic eigenvalue problems. SIAM J. Appl. Math. 15 (1967), 143.
M.J. Beran: Statistical Continuum Theories. Inter science Publishers, New York 1968.
J.M. Richardson: The application of truncated hi erarchy techniques in the solution of a stochastic linear differential equation.Proc.Symposia Appl.Math., vol. XVI, 1964,p. 290.
Helga Bunke: Stabilität bei stochastischen Diffe rentialgleichungssystemen. Z.ang. Math. Mech. 43 (1963), 63.
M. Kac: Probability theory. Proc. 1-st Symposium on Engineering Applications of Random Function Theory and Probability (J.L. Bogdanoff and F. Kozin, editors). J. Wiley and Sons, New York 1963, p. 37.
H. Parkus and J.L. Zeman: Some stochastic problems of thermoviscoelasticity. Proc. IUTAM Symposium on Thermoinelasticity. Glasgow 1968 (under press)
V.V. Bolotin:Statistical aspects in the theory of structural stability. Proc.Int.Conf. on Dynamic Stability of Structures. ( G.Herrmann, editor) Pergamon Press, New York 1967, p. 67.
J.R. Rice and F.P. Beer: First-occurrence time of high-level crossings in a continuous random process. J.Acoust.Soc.Ameri ca 39 (1966), 323.
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Parkus, H. (1969). Stochastic Stability. In: Random Processes in Mechanical Sciences. International Centre for Mechanical Sciences, vol 9. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2722-3_5
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DOI: https://doi.org/10.1007/978-3-7091-2722-3_5
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