Abstract
The nonlinear two-degree-of-freedom system under consideration consists of the linear oscillator with a relatively big mass, which is an approximation of some continuous elastic system, and of the vibro-impact oscillator with a relatively small mass, which is an absorber of the linear system vibrations. Analysis of nonlinear normal vibration modes shows that a stable localized vibration mode, which provides the vibration regime appropriate for the elastic vibration absorption, exists in a large region of the system parameters. In this regime, amplitudes of vibrations of the linear system are small, simultaneously vibrations of the absorber are significant.
Highlights
Numerous scientific papers contain a description and analysis of different devices for the absorption of elastic vibrations due to the importance of these problems in engineering
It is known that in many cases the absorption can be effective by using linear absorbers with big masses, but this is impossible to realize in most concrete systems
Oscillations of the two-DOF system are studied by methods of the nonlinear normal vibration mode (NNM) theory [13, 16, 25]
Summary
Numerous scientific papers contain a description and analysis of different devices for the absorption of elastic vibrations due to the importance of these problems in engineering. Oscillations of the two-DOF system are studied by methods of the nonlinear normal vibration mode (NNM) theory [13, 16, 25]. It is possible to select in the two-DOF nonlinear system under consideration the nonlocalized normal mode when the vibration amplitudes of the main linear subsystem and essentially nonlinear absorber are comparable, and the localized normal mode. The localized NNM, when the main linear system and absorber have small and large vibration amplitudes, respectively, is appropriate for the absorption. Note that the NNM approach was used earlier in some problems of the linear vibration absorption in systems containing the absorber with a cubic nonlinearity and the snap-through truss as an absorber [2, 3, 17]. The regions in the system parameter space, where the nonlocalized mode is unstable and the localized mode, appropriate to the absorption, is stable are selected
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