Vibrational Interactions When Mounting Several Rotors on an Elastic Base

The vibrations that arise in a system when several rotors with a small spread of dynamic characteristics are mounted on the elastic base are studied. Symmetrical frame structures with both linear and nonlinear elastic characteristics are considered as a base. It is shown that, in these systems, the interaction of different vibration modes occurs due to the low asymmetry, and unstable resonance modes with sharp jumps in vibration amplitudes occur at certain rotor rotation speeds. A system consisting of four rotors mounted on an elastic square shock-absorbing frame is analyzed. The conditions for the occurrence of unstable modes and the most dangerous rotor rotation speeds are found. The calculated and theoretical results are given. The mathematical apparatus of the theory of representation of symmetry groups is used for analytical studies of a symmetric system.