A PHYSICAL EXPLANATION OF THE DESTABILIZING EFFECT OF DAMPING

In this paper, the destabilization due to small damping of the followe r force system, known as Beck's problem, and of the cantilevered pipe conveying fluid system, two nonconservative systems, is considered. In stead of looking for a mathematical explanation, e.g., the evolution o f the eigenvalues with different parameters, a more ''physical'' expla nation is provided. It is shown that it is of particular interest to f ocus on the different modes of vibration and to understand how they ev olve when damping is varied. Also, based on energy considerations, the key factors influencing stability are highlighted, e.g., the phase an gles between the different coordinates. In the case of the pipe convey ing fluid, the methodology developed and insight gained help explain t he presence of ''jumps'' in the stability curves, that are known to pl ay an important role in the linear and nonlinear dynamics of this syst em.