NONLINEAR NORMAL VIBRATION MODES AND ITS APPLICATIONS IN SOME APPLIED PROBLEMS
Yuri Mikhlin, Sergei Mitrokhin
Nonlinear normal vibration modes (NNMs) are a generalization of normal vibrations in linear systems. In conception of NNMs by Kauderer-Rosenberg all position coordinates can be defined from any one of them. In conception of NNMs by Lyapunov-Shaw-Pierre all phase coordinates can be defined from two selected ones. Curvilinear trajectories of NNMs in a configuration space, or in a phase space, can be obtained as power series.
The NNMs theory are used to study vibrations of some linear structure attached with the single-DOF nonlinear absorbers with small masses. An essentially nonlinear oscillator, a snap-through truss with three equilibrium positions, and a vibro-impact oscillator are considered as absorbers. Construction and stability analysis of the localized and non-localized NNMs are made. If the localized mode is stable, and the non-localized vibration mode is unstable, the vibration energy is concentrated in the absorber.
Free damped oscillations of the double tracked road vehicle with a nonlinear response of the suspension can be considered by the NNMs theory too. The 7-DOF nonlinear model is used to analyze the suspension dynamics with smooth characteristics. The quarter-car model are considered for a case of the non-smooth characteristic of the shock absorber.