Nonstationary Response of Linear Time-Varying Dynamical Systems to Random Excitation

[+] Author and Article Information
F. Y. M. Wan

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass.

J. Appl. Mech 40(2), 422-428 (Jun 01, 1973) (7 pages) doi:10.1115/1.3423000 History: Received January 01, 1972; Revised July 01, 1972; Online July 12, 2010


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.

Copyright © 1973 by ASME
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