Normal vibration modes in nonlinear system with pendulum absorber

Authors

Keywords:

Pendulum systems, nonlinear normal vibration modes, vibration absorption

Abstract

To analyze the dynamics of a system with pendulum absorber we used the method of nonlinear normal vibration modes (NNMs) based on construction of trajectories of solutions in the configuration space in the form of a series by the small parameter, and some selected coordinate. The method of nonlinear normal vibration modes allows to analyze vibrations of pendulum systems for both small and large vibration amplitudes. The coupled (non-local) and the localized vibration modes are selected in the system. In the second case, the biggest part of the vibration energy is concentrated in the pendulum absorber, therefore localized mode is preferable for absorption of the elastic subsystem vibrations. The construction of the NNMs has been made and their stability has been studied by methods based on the Mathieu equation, Hill equations and Hill determinants. We constructed boundaries of the regions of stability of the NNMs in the system parameters plane. Loss of stability of the coupled vibration mode leads to a transfer to other vibration modes. It is showed that the localized vibration mode is the most favorable for vibration absorption, and the mode is stable in a wide range of the system parameters and vibration amplitudes.

Author Biography

Ю. В. Михлин, National Technical University "Kharkiv Polytechnic Institute"

Doctor of Physical and Mathematical Sciences

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Published

2014-11-28

Issue

Vol. 17 No. 3 (2014)

Section

Dynamics and Strength of Machines

License

Copyright (c) 2015 А. А. Клименко, Ю. В. Михлин

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