An eigenvector expansion method for the solution of motion containing fractional derivatives

Journal of Applied Mechanics, Transactions ASME

Volumn 64, Issue 3, 1997, Pages 629-635

  Suarez, L E ^a   Shokooh, A ^a  

^a UNIVERSITY OF PUERTO RICO   (Puerto Rico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003001893     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2788939     Document Type: Article

References (22)

1. Bagley, R. L., 1979, “Applications of Generalized Derivatives to Viscoelasticity,” Technical Report AFML-TR-79-4103, Air Force Materials Laboratory, Wright-Patterson Air Force Base, OH.
2. Bagley, R. L., and Torvik, P. J., 1979, “A Generalized Derivative Model for an Elastomer Damper,” The Shock and Vibration Bulletin, Vol. 49, Part 2, pp. 135-143.
3. Bagley, R. L., and Torvik, P. J., 1983, “A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity,” Journal of Rheology, Vol. 27, No. 3, pp. 201-210.
4. Bagley, R. L., and Torvik, P. J., 1983, “Fractional Calculus-A Different Approach to the Analysis of Viscoelastically Damped Structures,” AJAA Journal, Vol. 21, No, 5, pp. 741-748.
5. Bagley, R. L., and Torvik, P. J., 1985, “Fractional Calculus in the Transient Analysis of Viscoellastically Damped Structures,” AIAA Journal, Vol. 23, No. 6, pp. 918-925.
6. Bagley, R. L., and Torvik, P. J., 1986, “On the Fractional Calculus Model of Viscoelastic Behavior,” Journal of Rheology, Vol. 3, No. 1, pp. 133-155.
7. Gaul, L., Klein, P., and Kemple, S., 1989, “Impulse Response Function of an Oscillator with Fractional Derivative in Damping Description,” Mechanics Research Communications, Vol. 16, No. 5, pp. 297-305.
8. Gaul, L., Klein, P., and Kemple, S., 1991, “Damping Description Involving Fractional Operators,” Mechanical Systems and Signal Processing, Vol. 5, No. 2, pp. 8-88.
9. Koh, C. G., and Kelly, J. M., 1990, “Application of Fractional Derivatives M. Seismic Analysis of Base-Isolated Models,” Earthquake Engineering and Structural Dynamics, Vol. 19, pp. 229-241.
10. Lazan, B. J., 1968, Damping of Materials and Members in Structural Mechanics, Pergamon Press, New York.
11. Nashif, A. D., Jones, D. I. G., and Henderson, J. P., 1985, Vibration Damping, John Wiley and Sons, New York.
12. Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, New York.
13. Padovan, J., 1987, “Computational Algorithms for Finite Element Formulation Involving Fractional Operators,” Computational Mechanics, Vol. 2, pp. 271-287.
14. Rogers, L., 1983, “Operators and Fractional Derivatives for Viscoelastic Constitutive Equations,” Journal of Rheology, Vol. 27, No. 4, pp. 351-372.
15. Rogers, L., 1986, “Damping as a Design Parameter,” Mechanical Engineering Magazine, ASME, New York.
16. Ross, B., 1977, “Fractional Calculus,” Mathematics Magazine, Vol. 50, No. 3, pp. 115-122.
17. Shokooh, A., and Suarez, L., 1994. “On the Fractional Derivative Modeling of Damping Materials,” Technical Report prepared for NASA Langley, College of Engineering, University of Puerto Rico, Mayaguez, PR.
18. Shokooh, A., and Suarez, L., 1996, “A Comparison of Numerical Methods Applied to Fractional Model of Damping Materials,” Journal of Vibration and Control, submitted for publication.
19. Suarez, L., and Shokooh, A., 1995, “Response of Systems with Damping Materials Modeled Using Fractional Calculus,” ASME Applied Mechanics Review, Vol. 48, No. 11, Part 2, pp. S118-S127.
20. Suarez, L., Shokooh, A., and Arroyo, J., 1995, “Finite Element Analysis of Damping Materials Modeled by the Fractional Derivative Method,” Technical Report prepared for NASA Langley, College of Engineering, University of Puerto Rico, Mayaguez, PR.
21. Torvik, P. J., and Bagley, R. L., 1984, “On the Appearance of the Fractional Derivative in the Behavior of Real Materials,” ASME Journal of Applied Mechanics, Vol. 51, pp. 294-298.
22. Wolfram Research, Inc., 1993, Mathematica: A System for Doing Mathematics by Computer, Champaign, IL.