Volkova S. Modeling of non-linear systems with pulse excitations.

The non-linear systems with pulse excitations. Development and analysis of nonlinear mathematical models for systems with pulse excitations, creation and substantiation the methods of an analytical and numerical research of these systems behavior. The method of a non-smooth transformation of argument. The thesis deals with dynamics of nonlinear mechanical and physical systems under periodic impulse excitation. A preliminary stage of study is based on the special non-smooth (saw-tooth) transformation of the time parameter. The transformation eliminates discontinuous terms from the differential equations of motion and hence significantly improves its structure for both analytical and numerical analysis of the models. The technique is implemented for different practically important systems such as parametrically excited moved of Duff'ing system, a double-pendulum model of the liquid sloshing phenomenon in moving tanks subjected to the periodic impulsive loading, etc. The results show that the dynamics re lated strongly depends on the systems parameters and can perform periodic, quasi-periodic and quite complicated irregular stochastic-like regimes. It has been shown that the technique can be applied to study the self-excited oscillation of the Van-der-Paul's model under external series of the Dirac's impulses.