Energy and Nonlinear Dynamics of Hybrid Systems

Abstract

The transmission of energy between subsystems coupled in hybrid system is very important for different applications. For first as an introduction, by using the author's previously published references and that of her students, a short survey of an analytical study of the energy transfer between coupled subsystems is presented as a basis of this chapter. An analytical study of the mechanical energy transfer between two coupled subsystems, as well as, between two or more coupled rotation motions is presented. For starting, an analytical analysis of the mechanical energy transfer between a linear and a nonlinear oscillators of a hybrid system (see Refs. by Hedrih (Stevanovi´ 2002 (10, 11, 15-18, 20, 24)) in the free, as well as forced, vibrations of a different types of interconnections between subsystems is presented. Coupling element between subsystems of the considered hybrid systems are standard light elements with elastic, viscoelastic, hereditary, or creeping properties as well as dynamical constrain element realized by rolling element with inertia properties. Using Krilov-Bogolyubov-Mitropolskiy's asymptotic method, both the solutions in the first approximation and the system of nonlinear-coupled differential equations for the corresponding number of excited amplitudes and phases of multifrequency free as well as forced regimes are derived. By means of this asymptotic approximation of differential equations for the amplitudes and phases for forced vibrations of the coupled oscillators, the mutual influence of the nonlinear harmonics and energy transient were analyzed. The Lyapunov exponents corresponding to the each of two eigen like nonlinear modes are expressed by using energy of the corresponding eigen time components. A generalization of an analytical analysis of the transfer energy between linear and nonlinear oscillators for forced vibrations with different type constraints as a