Energy interaction between linear and nonlinear oscillators (energy transfer through the subsystems in a hybrid system) - Hedrih (Stevanović), K. (Український математичний журнал, 2008)
The study of the transfer of energy between subsystems coupled in hybrid system is very important for different applications. This paper presents an analytical analysis of the transfer of energy between linear and nonlinear oscillators for free vibrations when oscillators are statically, as well as dynamically, connected into double-oscillator system, as the two new hybrid systems, every with two degrees of freedom. The analytical analysis showed that the elastic connection between oscillators caused the appearance of a like two-frequency regime of time function, and that the energy transfer between subsystems appears. Also, the dynamical linear constraint between oscillators, each with one degree of freedom, coupled in hybrid system changes dynamics from single frequency regimes into like twofrequency regimes. The dynamical constraint as a connection between subsystems is realized by rolling element with inertia properties. In this case, an analytical analysis of the transfer energy between linear and nonlinear oscillators for free vibrations is also performed. The two Lyapunov exponents corresponding to each of two eigen modes are expressed by using energy of the corresponding eigen time component.