Regular and chaotic dynamics of nonlinear systems with parametric excitation

The talk deals with vibrations caused by parametric or autoparametric excitations. This kind of vibrations may appear in many practical engineering systems. Then different untypical and intuitively unpredicted interactions may be observed. The first example considered in the talk presents regular and chaotic dynamics of an autoparametric system with pendulum and a magnetorheological damper. Analytical, numerical and experimental results near the instability zones will be demonstrated. The second example presents dynamics and possible vibration modes of an autoparametric composite beam structure with essentially different stiffness in two orthogonal directions. This example is under current study and methods of the problem reduction under discussion. The final part of the talk concerns analysis of new dynamic phenomena obtained for oscillatory systems, taking into account different excitations, self-, parametric and external, acting in the same time. Periodic, quasi-periodic and chaotic oscillations, as well as, essential qualitatively changes near the main parametric resonance are presented for the considered models.