Mean-square stability of elastic bodies in supersonic flow

Author Type

Faculty

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Journal of Sound and Vibration

Publication Status

Version of Record

Abstract

The mean-square stability of elastic bodies in supersonic flow is studied. The external load consists of pressure fluctuations in the turbulent boundary layer, and of the pressure perturbation depending on the elastic body deformations according to the "piston theory". For solving the stochastic boundary problem, both the given and sought random functions are resolved in the modes of vibration of an elastic system in vacuo. Galerkin's method yields an infinite set of linear algebraic equations for the response spectra, solved by reduction. It is shown that the reduced set is stable in the mean-square if the corresponding deterministic set is asymptotically stable, and moreover if a certain inequality is satisfied regarding the response characteristics. It is also shown that the mean-square stability falls within the pre-flutter range of the system parameters. The actual computations for the mean-square stability of a clamped-clamped beam in turbulent supersonic flow in two- and three-mode approximations will be presented at a later date. © 1974 Academic Press Inc. (London) Limited.

First Page

67

Last Page

78

DOI

10.1016/S0022-460X(74)80074-X

Publication Date

3-8-1974

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