Energy analysis in a nonlinear hybrid system containing linear and nonlinear subsystems coupled by hereditary element

Energy transfer between subsystems coupled by standard light hereditary element in hybrid system is very important for different engineering applications, especially for dynamical absorption. An analytical study of the energy transfer between coupled linear and nonlinear oscillators in the free vibrations of a viscoelastically connected double-oscillator system as a new hybrid nonlinear system with two and half degrees of freedom is pointed out. The analytical study shows that the viscoelastic–hereditary connection between oscillators causes the appearance of like two-frequency regimes of subsystem's vibrations and that the energy transfer between subsystems appears. The Lyapunov exponents corresponding to each of two eigenmodes of the hybrid system, as well as to the subsystems are obtained and expressed by using energy of the corresponding eigentime components. The Lyapunov exponents are measures of the vibration processes stability in the hybrid system and in component subsystem vibrations. In Honor of Giuseppe Rega and Fabrizio Vestroni on the Occasion of their 60th Birthday.