Grazing instabilities and post-bifurcation behavior in an impacting string.
A theoretical and experimental investigation of the nonlinear dynamic response of a periodically excited string subject to a knife-edge amplitude restraint is presented. The amplitude restraint creates an impact condition as the amplitude of the response grows. The focus of this work is on the influence of a grazing instability; this zero-velocity impact event leads to complicated, post-bifurcation behavior ranging from multifrequency, periodic motion to chaos. In addition to looking at the response numerically, parameter combinations leading to an incidence of grazing are clearly identified in the excitation force excitation frequency parameter space using a multiple scales perturbation analysis. Modeling issues, numerical difficulties, and experimental limitations are also discussed.