Stability and Bifurcations Analysis for 2-DOF Vibroimpact System by Parameter Continuation Method. Part I: Loading Curve

摘要

Vibroimpact system dynamic behaviour is studied by numerical parametric continuation technique combined with shooting and Newton-Raphson's methods. The technique is adapted to two-body two-degree-of-freedom vibroimpact system under periodic excitation. Impact is simulated by nonlinear contact interaction force based on Hertz's contact theory. Stability or instability of obtained periodic solutions is determined by monodromy matrix eigenvalues based on Floquet's theory. Analysis of dynamic behaviour for specific vibroimpact system was performed. The instability zones, different oscillatory regimes and bifurcation points were found. Poincare sections were also constructed.