Abstract
Existence and Stability of the Periodic Orbits Induced by Grazing Bifurcation in a Cantilever Beam System with Single Rigid Impacting Constraint
Highlights
Because of the existence of collision, vibro-impact system is strongly nonlinear and nonsmooth,and has various nonclassical bifurcations caused by grazing
Dankowicz[5] studied a class of micro-drive devices, proposed three types of co-dimension one bifurcation types, and used the discontinuous mapping method to predict the dynamic characteristics of the grazing bifurcation based on the system properties
Considering a cantilever beam system with a single impacting constraint, we uncover the existence and stability of periodic orbits induced by grazing
Summary
Because of the existence of collision, vibro-impact system is strongly nonlinear and nonsmooth,and has various nonclassical bifurcations caused by grazing. Emans[21] first introduced the nonlinear restoring force to establish the nonlinear elastic impact model, and studied the chaotic phenomenon by numerical simulation. Huangfu[23] conducted a numerical analysis of unilateral grazing bifurcation and verified that the local discontinuous mapping is effective when it contains nonlinear terms. This paper focuses on the existence and stability of the periodic orbits induced by grazing in a cantilever beam system with impacts. 3, the discontinuous mapping method is used to established the Poincaré compound mapping, and a combination of inhomogeneous equations and inequations is obtained to determine the existence and stability of the periodic orbits induced by grazing bifurcations.
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