Abstract
Based on the research of a periodic forced system with soft impacts, the piecewise properties of the soft-impacts system, such as asymmetric motion and singularity, were analyzed by using the Poincaré map and Runge-Kutta numerical simulation method. The routes from periodic motions to chaos, via Hopf bifurcation and grazing bifurcation, were investigated thoroughly. In the case of large constraint stiffness, the Hopf bifurcation is observed in the periodic forced system with soft impacts. The clearances of the system are the main reasons for influencing the chaotic motion. For small clearances, the grazing bifurcations bring about asymmetric motion and singularity. The steady 1-1-1 period orbits will exist within a wideband frequency range when appropriate system parameters are chosen.
Highlights
The soft impacts induce extensive oscillation in mechanical systems
The nonlinear characteristics of the periodic forced system with soft impacts were analyzed with special attention on stability of periodic motion, grazing bifurcation, period-doubling bifurcation, Hopf bifurcation and chaotic motion, etc
(1) The 1-1-1 motion, in most cases, underwent grazing bifurcation or Hopf bifurcation to chaos with a change in the system parameters
Summary
The soft impacts induce extensive oscillation in mechanical systems. Such piecewise linear systems are capable of exhibiting classically non-linear behavior such as grazing bifucations. It is necessary to be able to accurately model the dynamics of mechanical systems with soft impacts and clearances, to enlarge profitable effects and minimize adverse effects. Nordmark [2] developed systematic methods for investigating grazing dynamics and attendant bifurcations of the piecewise linear and vibro-impact systems. In wheel-rail impacts of railway coaches Luo et al [9], Jeffcott rotor with bearing clearance Karpenko et al [10], gears transmissions Alshyyab, and Kahraman [11], small vibro-impact pile driver Luo and Yao [12], etc., impacting models have been proved to be useful. The influences of clearances on periodic motions and bifurcations of the periodic forced system are discussed in detail
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