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.
KeywordsWhite Noise Asymptotic Stability Random Function Image Point Parametric Excitation
Unable to display preview. Download preview PDF.
- J.L.Bogdanoff and F.Kozin: Moments of the output of linear random systems. J.Acoust. Soc.America 34 (1962), 1063.Google Scholar
- J.B. Keller: Stochastic equations and wave propaga tion in random media. Proc.Symposia Appl. Math., vol.XVI, 1964,p. 145.Google Scholar
- 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.Google Scholar
- H. Parkus and J.L. Zeman: Some stochastic problems of thermoviscoelasticity. Proc. IUTAM Symposium on Thermoinelasticity. Glasgow 1968 (under press)Google Scholar
- 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.Google Scholar