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Self-excited systems: Analytical determination of limit cycles. (English) Zbl 1142.70010
Summary: The determination of amplitude and period of limit cycles is a crucial question in nonlinear mechanics. Recently [the author, in B. Bhushan (ed.), Nato ASI Series E 311, 305–311 (2001)], a van der Pol oscillator containing a periodic potential has been considered as a suitable self-excited system in tribological studies. Analytical expressions for amplitude and period of limit cycles for such modified van der Pol oscillator are calculated making use of He’s variational method and Krylov-Bogoliubov-Mitropolsky method. The analytical results are then compared to the correspondent numerical results, showing the goodness of the two methods in the range of application.

MSC:
70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
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