Impulse Moments Influence on Single-Frequency Torsional Oscillations of Nonlinear Flexible Bodies

The method of analytical study of the influence of impulse moments on nonlinear torsional oscillations of a homogeneous constant cross-section of a body under classical boundary conditions of the first, second, and third types have been developed. When the flexible material properties meet the body close to the power law of flexibility, mathematical models of the process have been obtained. It is the boundary value problem for an equation of hyperbolic type with a small parameter at the discrete right-hand side. The latter expresses the effect of pulse momentum on the oscillatory process. Under the effect of periodic pulse momentum on a flexible body, resonant and non-resonant processes are possible. Resonant processes occur when the amplitude of natural oscillations approaches a fixed value. The peculiarities of resonant oscillations are established. The amplitude of passing through the primary resonance is significant for larger values of the nonlinearity parameter and, in the case of the action of pulse momentum, closer to the middle of the body. If the initial perturbation amplitude is less than the amplitude at which the resonance occurs in the presence of only internal forces of viscous friction. So, the external periodic impulse moments of resonance processes have occurred. The extreme case confirms the reliability of the results obtained related to the dynamics of the respective objects under the continuous action of autonomous perturbation.