Self-excited systems: Analytical determination of limit cycles

The determination of amplitude and period of limit cycles is a crucial question in non-linear mechanics. Recently, a van der Pol oscillator containing a periodic potential has been considered as a suitable self-excited system in tribological studies. Analytical expressions for the amplitude and the period of limit cycles for such modified van der Pol oscillator are calculated making use of the He’s variational method and the Krylov–Bogoliubov–Mitropolsky (KBM) method. The analytical results are then compared to numerical correspondent results, showing the goodness of the two methods in the range of application.