Dynamics of nonlinear dissipative systems in the vicinity of resonance

• Spring–mass–pendulum system and 2-DOF system with nonlinear absorber are considered.
• Analysis of resonance vibrations is made by using the so-called reduced system.
• Evolution of vibration modes and energy transient are studied.
• Transient nonlinear modes existing only for some instant of time are selected.

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.