DISCONTINUOUS BIFURCATIONS OF A CANTILEVER BEAM SYSTEM WITH CLEARANCE RESTRICTIONS

A cantilever beam with clearance restrictions is widely used in mechanical and engineering design. the quality of its dynamic properties directly reflects the operation quality of the overall system, and it is a key factor in determining whether the overall system can operate safely and efficiently. Study on the multi-parameter dynamics of cantilever beam collision system can achieve the optimal design of the dynamic characteristics and function target. Considering the cantilever beam system with clearance restrictions. The global Poincaré map composed of smooth flow maps and the Jacobian matrix are constructed. Based on Floquet theory and grazing conditions, the existence regions of various types of periodic and chaotic attractors in the two-parameter plane are obtained by applying numerical method. The transition characteristics of adjacent symmetric period-1 attractors through the beat motion zones and the formation mechanism of coexisting attractors are revealed by combining the numerical simulation, continuation shooting approach and cell mapping method. The important roles of unstable periodic attractors in the dynamic evolutions of the system are revealed, as well as different types of discontinuous bifurcations, such as crises, hysteresis, saddle-node-type period-doubling bifurcations and subcritical pitchfork bifurcations. The results indicate that there are nine types of discontinuous bifurcations in the evolutions of periodic attractors in the elastic impact system with symmetric clearances. The coexistences of multiple attractors are more common due to the occurrence of pitchfork bifurcations. The simultaneous interior crises of two coexisting chaotic attractors can be induced by a pair of asymmetric unstable periodic orbits. The definitions of pitchfork-type grazing bifurcation and nine types of discontinuous bifurcations will further enrich the dynamics of non-smooth systems.