Stability and Discontinious Bifurcations in Vibroimpact System. Numerical investigations

      Аннотация: There is detailed numerical investigation of dynamical behaviour of two-body 2-DOF vibroimpact system under periodical excitation in this work. We consider systems of two kinds: with rigid and soft impacts. We compare two ways of impact simulation and evaluate the possibility of their application for these systems. It is simulation by relations of stereomechanic shock theory and by nonlinear interaction force based on quasistatic contact Hertz’s theory. We use numerical parameter continuation method for construction the loading curves and amplitude-frequency responses. We find out instability zones, bifurcations, particularly the discontinuous bifurcations which are the dangerous ones. We obtain the periodic, quasiperiodic, chaotic regimes of system motion. We construct Poincare sections, Fourier spectrums, and Lyapunov exponents for confirming the periodicity or chaoticity of obtained regimes. We show how the system parameters modification may change the impact kind in system ? from rigid to soft, and how the dynamic characteristics change thereat. Description is accompanied by the great numbers of graphs and Tables that illustrate the results of huge numerical experiments volume.

Ключевые слова: Multiplier, Nonlinear, Stability, Vibroimpact system, rigit and soft contact, discontinuous bifurcation, Hertz’s theory