Abstract
The behavior of nonlinear dissipative 2-DOF mechanical systems in the vicinity of resonance is studied in this paper. Namely, the free resonance vibrations of a spring–mass–pendulum system and the forced resonance vibrations of a 2-DOF dissipative system containing a nonlinear absorber are considered. A reduced system stated with respect to the system energy, the arctangent of the vibration amplitudes ratio, and the phase difference, is obtained and analyzed. The nonlinear normal mode approach is used in this analysis. Conditions for vibration energy localization are discussed.
Highlights
An investigation of the behavior of nonlinear systems in the presence of internal resonance is an important step in the solution of some theoretical and applied problems, in particular, problems of modal interaction and the localization of vibration energy
Internal resonance can lead to a loss of vibration mode stability, and to the appearance of new vibration regimes as a result of bifurcation
The interaction of vibration modes, their stability, the localization of energy and other important characteristics of dynamical process as all depend on time, since dissipative system energy decreases in time
Summary
An investigation of the behavior of nonlinear systems in the presence of internal resonance is an important step in the solution of some theoretical and applied problems, in particular, problems of modal interaction and the localization of vibration energy. In a series of papers by Vakakis, Manevitch, Gendelman, Bergman et al [11,12,13,14], a theoretical investigation and an experimental verification of the energy transfer and localization has been presented for different nonlinear systems. The interaction of vibration modes, their stability, the localization of energy and other important characteristics of dynamical process as all depend on time, since dissipative system energy decreases in time. An investigation of the stability and bifurcation of vibration modes is performed The evolution of such vibration modes, and the energy transfer from one mode to another one, are both considered. The localization of energy is discussed and analytical results are compared with numerical and numerical-analytical simulations
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