On the motion of a generalized Van der Pol oscillator: influence of the fracational-order restoring and damping force
Brennan, M.J., Kovacic, Ivana, Lopes Jr, V., Murphy, K., Petersson, B., Rizzi, S. and Yang, T. (eds.)
In Proceedings of the Tenth International Conference on Recent Advances in Structural Dynamics (RASD2010).
University of Southampton..
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A generalized van der Pol oscillator is considered, with the positive real power nonlinearities
in the restoring and damping force, including fractional powers. An analytical approach based
on the Krylov–Bogoliubov method is utilized to derive approximate expressions for the
amplitude of a limit cycle for small values of the damping coefficient. Matched asymptotic
expansions are used to study relaxation oscillations for larger values of the damping
coefficient. The influence of the powers of the restoring and damping force on the properties
of these oscillations is investigated.
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