Effect of dry friction on a parametric nonlinear oscillator

Parametrically excited oscillators are used in several domains, particular to improve the dynamical behaviour of systems like case parametric amplification or energy harvesting. Although dry friction is often omitted during system modelling due complexity its nonsmooth nature, it sometimes necessary account for this kind damping adequately represent motion. In paper, proposed investigate effect on a nonlinear oscillator. Using pendulum as example, problem formulated according Mathieu-Duffing equation. Semi-analytical developments using harmonic balance method and varying amplitudes find solutions equation their stability. These results validated thanks comparison with time integration simulations. Effects initial conditions basins attractions also studied these It found that trivial nontrivial oscillator including not connected, giving birth isolated periodic branches. Thus, both displacement phase between excitation must be carefully chosen reach solutions. Finally, based principle critical forcing amplitude frequency needed obtain friction.