Dynamics of an oscillator with both clearance and continuous non-linearities

On the response of a preloaded mechanical oscillator with a clearance: Period-doubling and chaos

“…All period-n and chaotic solutions lie within a critical range of F, and the oscillator acts as a nearly linear system outside this range. The regions of subharmonic and chaotic solutions on the ~'-~" map are more localized for the dead-zone nonlinearity than for cubic nonlinearity, suggesting that the prediction of the regions of nonlinear solutions could be easier for clearance nonlinearities, unless the contact stiffness is nonlinear [38]. Another difference is that period-m/n solutions (m/n is a fraction), which were reported for the Duffing's equation, do not seem to exist for the dead-zone nonlinearity.…”

A Spline Joint Formulation for Drive Train Torsional Dynamic Models

“…While continuously non-linear and simple piecewise linear or bi-linear systems have been studied extensively, piecewise non-linear systems like the one de"ned above by equation (13) for a spline joint have attracted very limited interest [10,11]. The current research of this author includes deriving analytical solutions to the formulation presented here and also incorporating it in the dynamic analysis of multi-degree-of-freedom drive train systems.…”

Vibration behavior optimization of planetary gear sets

“…In the last twenty years the most of dynamic models were focused on non-linear aspects. Kahraman and Singh [21][22][23][24] considered the effect of backlash and time varying mesh stiffness using harmonic balance method and digital simulation. A similar model was developed by Theodossiades and Natsiavas [25][26][27] who predicted chaotic behavior by means of numerical integration: such intermitted chaos and boundary crises.…”