Instability analysis in oscillators with velocity-modulated time-varying stiffness—Applications to gears submitted to engine speed fluctuations

A one degree-of-freedom model is set up which incorporates time-varying mesh stiffness functions and the influence of unsteady input rotations due to engine speed fluctuations. The stability of the associated parametrically excited system is analysed by calculating the monodromy matrix via a Newmark scheme. A piecewise constant and a sinusoidal mesh stiffness functions are considered and it is shown that additional side-band instability zones are generated because of frequency modulations. The influence of the mesh stiffness variations and damping is discussed.