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Nonlinear normal vibration modes and its applications in some applied problems
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Mikhlin, Y.V. Nonlinear normal vibration modes and its applications in some applied problems [Текст] / Mikhlin Y.V., Mitrokhin S. // Статті : - ENOC, 2011.
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Nonlinear normal vibration modes (NNMs) are a generalization of the normal vibrations in the 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 is used to study vibrations of some linear structure connected with the single-DOF nonlinear absorber. An essentially nonlinear oscillator, a snap-through truss with three equilibrium positions, and a vibro-impact oscillator are chosen as absorbers. Construction and stability analysis of the NNMs are presented. 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 is considered for a case of the non- smooth characteristic of the shock absorber.

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