A direct time-domain method is used to analyze the titled problem. Special attention is paid to a system characterized by a general second-order equation with variable coefficients. The equation of flapping motion of a rigid rotor blade advancing in atmospheric turbulence belongs to this class. Steady-state mean-square response to ideal white noise and to exponentially correlated excitation is obtained by a perturbation series solution in a stiffness parameter. An upperbound of the same is derived. Explicit solution for the correlation matrix is obtained by the two-variable expansion method. Specialized to the rotor blade problem, the results have led to some new information concerning the blade behavior in a certain range of rotating speed. They have also served as useful check cases for computer programs developed for more general problems. Higher-order equations and their applications are also discussed.
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June 1973
Research Papers
Nonstationary Response of Linear Time-Varying Dynamical Systems to Random Excitation
F. Y. M. Wan
F. Y. M. Wan
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass.
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F. Y. M. Wan
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass.
J. Appl. Mech. Jun 1973, 40(2): 422-428 (7 pages)
Published Online: June 1, 1973
Article history
Received:
January 1, 1972
Revised:
July 1, 1972
Online:
July 12, 2010
Citation
Wan, F. Y. M. (June 1, 1973). "Nonstationary Response of Linear Time-Varying Dynamical Systems to Random Excitation." ASME. J. Appl. Mech. June 1973; 40(2): 422–428. https://doi.org/10.1115/1.3423000
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