A Physical Explanation of the Destabilizing Effect of Damping

[+] Author and Article Information
C. Semler, H. Alighanbari, M. P. Païdoussis

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada

J. Appl. Mech 65(3), 642-648 (Sep 01, 1998) (7 pages) doi:10.1115/1.2789106 History: Received December 17, 1996; Revised February 11, 1998; Online October 25, 2007


In this paper, the destabilization due to small damping of the follower force system, known as Beck’s problem, and of the cantilevered pipe conveying fluid system, two nonconservative systems, is considered. Instead of looking for a mathematical explanation, e.g., the evolution of the eigenvalues with different parameters, a more “physical” explanation is provided. It is shown that it is of particular interest to focus on the different modes of vibration and to understand how they evolve when damping is varied. Also, based on energy considerations, the key factors influencing stability are highlighted, e.g., the phase angles between the different coordinates. In the case of the pipe conveying fluid, the methodology developed and insight gained help explain the presence of “jumps” p in the stability curves, that are known to play an important role in the linear and nonlinear dynamics of this system.

Copyright © 1998 by The American Society of Mechanical Engineers
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