We apply the method of averaging to study small, possibly nonlinear perturbations to a harmonic oscillator, particularly including fractional derivative damping. The averaging procedure here corresponds to the general or aperiodic case, and requires evaluation of Fresnel type integrals. We also describe a conceptually simple numerical scheme which can be used to verify the accuracy of the averaged equations. Systems studied are a linear, fractionally damped oscillator, a van der Pol type oscillator with a limit cycle, and a weakly nonlinear system forced sinusoidally near resonance. The averaged dynamics closely matches the full numerical solution in each case. It is discussed, in light of the averaged equations, why fractional damping is not equivalent to some simple effective traditional damping.
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ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 2–6, 2003
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-3703-3
PROCEEDINGS PAPER
Averaging for Oscillations With Light Fractional Order Damping
Pankaj Wahi,
Pankaj Wahi
Indian Institute of Technology, Bangalore, India
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Anindya Chatterjee
Anindya Chatterjee
Indian Institute of Technology, Bangalore, India
Search for other works by this author on:
Pankaj Wahi
Indian Institute of Technology, Bangalore, India
Anindya Chatterjee
Indian Institute of Technology, Bangalore, India
Paper No:
DETC2003/VIB-48386, pp. 721-727; 7 pages
Published Online:
June 23, 2008
Citation
Wahi, P, & Chatterjee, A. "Averaging for Oscillations With Light Fractional Order Damping." Proceedings of the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C. Chicago, Illinois, USA. September 2–6, 2003. pp. 721-727. ASME. https://doi.org/10.1115/DETC2003/VIB-48386
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