A Calculation Method on Bifurcation and State Parameter Sensitivity Analysis of Piecewise Mechanical Systems

Abstract

The paper proposes a novel calculation method on the sensitivity analysis of bifurcation parameters and states in a single-degree-of-freedom (SDoF) impacting system. It presents the causes to (non-) smooth bifurcations in virtue of parameter sensitivity analysis. The derivation of the system’s Poincaré mappings is used to integrate the Floquet matrix. It performs the identifications of the main and the most sensitive bifurcation parameters by disturbing the eigenvalues of Floquet matrix. Moreover, the ones that have appreciable effect on the dynamic characteristics of the system can be effectively identified from entire bifurcation parameters and states. The coexistence of distinct attractors is demonstrated with the parameter sensitivity analysis on the Floquet matrix associated with bifurcation parameters and states. It also considers the cooperating dynamic performance on the two-dimensional parameter space by varying different pairs of bifurcation parameters.