The effect of non-conservative forces on the stability of systems with multiple frequencies and the Nicolai paradox is investigated. The system is said to be stable if all eigenvalues are pure imaginary and simple or semi-simple. The occurrence of the conical singularity in the three-dimensional space of parameters is natural because the double real semisimple eigenvalue defines the singularity of the codimension in the bifurcation diagram of the family of nonsymmetric matrices. The destabilization phenomenon is similar to the step-like increase in the combination resonance zone with adding a small damping. The effect of the cross-section asymmetry on the stability in the absence of damping depends on the first vibration mode with the frequency. Due to equivalence of the stability problems, the inequality is valid also in the case of the tangential twisting moment.
展开▼
