A Physical Explanation of the Destabilizing Effect of Damping

Abstract

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.