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Abstract: The paper presents new results on instability of general rotating systems with small axial asymmetry and damping. Rotating systems with arbitrary finite degrees of freedom are considered. Instability conditions are derived for nonresonant and resonant rotation speeds characterized by simple and double eigenvalues. As an application, the stability problem of a rotating elastic shaft with small internal and external damping forces and asymmetric imperfections is studied. The numerical example shows validity and accuracy of the derived analytical formulae for the instability regions. [Copyright &y& Elsevier]

A linear vibrational system with multiple degrees of freedom subjected to parametric excitation is considered. It is assumed that the system is statically unstable but close to a critical point, the excitation amplitude and damping are small, and the excitation frequency is arbitrary. A new stabilization condition is derived in terms of integrals depending on eigenfrequencies and modes of the undisturbed conservative system and the symmetric excitation matrix. As a special case, an approximation for high-frequency excitation is deduced from this condition. Influence of damping on stabilization region is shown to be very small. Two examples for systems with one and two degrees of freedom are presented. It is shown that stabilization of statically unstable systems is possible for low, medium and high excitation frequencies. [Copyright &y& Elsevier]

In this paper we consider the combined effect of rotating and non-rotating asymmetries on a rotor under non-conservative loading, motivated by technical applications in which breaking of symmetries may be used to avoid self-excited vibrations. We consider a rotating disk with two translatory degrees of freedom describing the displacements of the center of the disk with respect to the axis of rotation and two rotational degrees of freedom describing the tilting angles with respect to the axis of rotation. It is shown that breaking of symmetries of the rotating and non-rotating restoring terms has opposite effects for the stability behavior of translatory and rotational motions. Thus, if neither the translatory nor rotational degrees of freedom are dominant, it will be difficult to find robust designs against self-excited vibrations using the approach of breaking symmetries. [ABSTRACT FROM AUTHOR]