Wahi, Pankaj and Chatterjee, Anindya (2004) Averaging Oscillations with Small Fractional Damping and Delayed Terms. In: Nonlinear Dynamics, 38 (1-2). pp. 3-22.
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We demonstrate the method of averaging for conservative oscillators which may be strongly nonlinear, under small perturbations including delayed and/or fractional derivative terms. The unperturbed systems studied here include a harmonic oscillator, a strongly nonlinear oscillator with a cubic nonlinearity, as well as one with a nonanalytic nonlinearity. For the latter two cases, we use an approximate realization of the asymptotic method of averaging, based on harmonic balance. The averaged dynamics closely match the full numerical solutions in all cases, verifying the validity of the averaging procedure as well as the harmonic balance approximations therein. Moreover, interesting dynamics is uncovered in the strongly nonlinear case with small delayed terms, where arbitrarily many stable and unstable limit cycles can coexist, and infinitely many simultaneous saddle-node bifurcations can occur.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Springer.|
|Keywords:||Delay differential equations;Fractional derivatives; Harmonic balance;Averaging;Strongly nonlinear oscillations; Saddle-node bifurcations|
|Department/Centre:||Division of Mechanical Sciences > Mechanical Engineering|
|Date Deposited:||30 Jun 2006|
|Last Modified:||19 Sep 2010 04:29|
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