An extension of the τ-decomposition method is used to predict the stability of a continuous system subjected to nonconservative loading. The technique is implemented through Ritz-finite element discretization. The stability of a flexible rocket (or beam) with a controlled orientation thrust vector (or follower force) is examined with respect to finite time delay in the control mechanism. Higher mode instabilities in the rocket are observed in the sample problem and are treated satisfactorily in the technique. Both buckling and flutter conditions are determined from eigenvalue trajectories in the complex plane.
Time Delay Instabilities in Large Order Systems With Controlled Follower Forces
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Matsumoto, G. Y., and Mote, C. D., Jr. (December 1, 1972). "Time Delay Instabilities in Large Order Systems With Controlled Follower Forces." ASME. J. Dyn. Sys., Meas., Control. December 1972; 94(4): 330–334. https://doi.org/10.1115/1.3426616
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