Existence and stability of the periodic orbits induced by grazing bifurcation in a cantilever beam system with single rigid impacting constraint

Grazing, which can induce many nonclassical bifurcations, is a special dynamic phenomenon in some non-smooth dynamical systems such as vibro-impact with clearance. In this paper, the existence and stability of periodic orbits induced by grazing bifurcation cantilever beam system impacts are uncovered. Firstly, Poincaré mapping obtained adopting discontinuous method. Then, means shooting method, determined, followed acquisition Jacobian matrix case non-impact subsequently. addition, for various impacting patterns, combination inhomogeneous equations inequations to determine period after grazing, criterion grazing-induced given. Numerical results verify effectiveness theoretical analysis. What more, we also give conjecture about relationship between eigenvalues type when imaginary numbers.