Averaging for oscillations with light fractional order damping

Proceedings of the ASME Design Engineering Technical Conference

Volumn 5 A, Issue , 2003, Pages 721-727

  Wahi, Pankaj ^a   Chatterjee, Anindya ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DAMPING; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; INTEGRATION; INTERPOLATION; LINEAR SYSTEMS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PROBLEM SOLVING; RUNGE KUTTA METHODS; VIBRATIONS (MECHANICAL);

FRACTIONAL DERIVATIVES; INTERPOLANTS;

OSCILLATIONS;

EID: 1842634159     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/detc2003/vib-48386     Document Type: Conference Paper

References (14)

1. Bagley, R. L., and Torvik, P. J., 1983, "A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity", Journal of Rheology, 27 (3), pp. 201-210.
2. Bagley, R. L., and Torvik, P. J., 1983, "Fractional Calculus - A Different Approach to the Analysis of Viscoelastically Damped Structures", AIM Journal, 21 (5), pp. 741-748.
3. Bagley, R. L., and Torvik, P. J., 1985, "Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures", AIM Journal, 23 (6), pp. 918-925.
4. Koeller, R. C., 1984, "Application of Fractional Calculus to the Theory of Viscoelasticity", ASME Journal of Applied Mechanics, 51, pp. 299-307.
5. Gaul, L., Klein, P., and Kemple, S., 1989, "Impulse Response Function of an Oscillator with Fractional Derivative in Damping Description", Mechanics Research Communications, 16 (5), pp. 297-305.
6. Suarez, L. E., and Shokooh, A., 1997, "An Eigenvector Expansion Method for the Solution of Motion Containing Fractional Derivatives", ASME Journal of Applied Mechanics, 64 (3), pp. 629-635.
7. Koh, C. G., and Kelly, J. M., 1990, "Application of Fractional Derivatives to Seismic Analysis of Base-isolated Models", Earthquake Engineering and Structural Dynamics, 19, pp. 229-241.
8. Yuan, L., and Agrawal, O. P., 1998, "A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives", Proceedings of 1998 ASME Design Engineering Technical Conferences, September 13-16, Atlanta, Georgia.
9. Li, G., Zhu, Z., and Cheng, C., 2001, "Dynamical Stability of Viscoelastic Column with Fractional Derivative Constitutive Relation", Applied Mathematics and Mechanics, 22 (3), pp. 294-303.
10. Sanders, J. A., and Verhulst, F., 1985, Averaging Methods in Nonlinear Dynamical Systems, Springer-Verlag, New York.
11. Wahi, P., and Chatterjee, A., 2003, "Averaging Nonlinear Oscillations with Small Fractional Damping and Delayed Terms", Draft under preperation.
12. Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus - theory and applications of differentiation and integration to arbitrary order, Academic Press, New York.
13. Rand, R. H., 2000. Lecture Notes on Nonlinear Vibrations, version 34. Available online at http://www.tam.cornell.edu/randdocs/.
14. Verhulst, F., 1990, Nonlinear Differential Equations and Dynamical Systems, Springer-Verlag, Berlin.