Nonlinear Vibrations of Fractionally Damped Systems

Nonlinear Dynamics

Volumn 16, Issue 4, 1998, Pages 321-336

  Padovan, Joe ^a   Sawicki, Jerzy T ^b  

^a The University of Akron   (United States)

^b Cleveland State University   (United States)

Author keywords

Duffing's equation; Fractionally damped; Nonlinear systems; Perturbation procedure

Indexed keywords

DAMPING; HYSTERESIS; MATHEMATICAL OPERATORS; NONLINEAR SYSTEMS; OSCILLATIONS; PERTURBATION TECHNIQUES;

DUFFING'S EQUATION; FRACTIONALLY DAMPED SYSTEMS; LINDSTEDT-POINCARE PERTURBATION PROCEDURE;

VIBRATIONS (MECHANICAL);

EID: 0032141482     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008289024058     Document Type: Article

References (16)

1. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.
2. Meirovitch, L., Analytical Methods in Vibrations, Macmillan, New York, 1967.
3. Fertis, D. G., Mechanical and Structural Vibration, Wiley, New York, 1995.
4. Simhambhatla, M. and Leonov, A. I., 'The extended Pade-Laplace method for efficient discretization of linear viscoelastic spectra', Rheologien Acta 32, 1993, 584-600.
5. Kwon, Y and Leonov, A. I., 'Stability constraints in the formulation of viscoelastic constitutive equations', Journal of Non-Newtonian Fluid Mechanics 58, 1995, 25-46.
6. Golden, J. M. and Graham, G. A. C., Boundary Value Problems in Linear Viscoelasticity, Springer-Verlag, Berlin, 1988.
7. Kwon, Y and Leonov, A. I., On Hadamard-type stability of single-integral constitutive equations for viscoelastic liquids', Journal of Non-Newtonian Fluid Mechanics 41, 1993, 77-91.
8. Padovan, J. and Sawicki, J. T., 'Diophantine type fractional derivative representation of structural hysteresis, Parti: Formulation', Computational Mechanics 19(5), 1997, 335-341.
9. Sawicki, J. T. and Padovan, J., 'Diophantine type fractional derivative representation of structural hysteresis, Part II: Fitting', Computational Mechanics 19(5), 1997, 341-356.
10. Bagley, R. L. and Calico, R. A., 'Fractional order state equations for the control of viscoelastically damped structures', Journal of Guidance Control and Dynamics 14, 1991, 304-311.
11. Bagley, R. L. and Torvik, P. J., 'Fractional calculus - A different approach to the analysis of viscoelastically damped structures', AIAA Journal 21(5), 1983, 741-748.
12. Enelund, M. and Josefson, B. L., 'Time-domain FE-analysis of viscoelastic structures having constitutive relations involving fractional derivatives', in Proceedings of 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Salt Lake City, UT. Also: AIAA Journal 38, 1997, 1630-1637.
13. Enelund, M. and Josefson, B. L., 'Time-domain FE-analysis of viscoelastic structures having constitutive relations involving fractional derivatives', in Proceedings of 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Salt Lake City, UT. Also: AIAA Journal 38, 1997, 1630-1637.
14. Oldham, K. B. and Spanier, J., The Fractional Calculus, Academic Press, New York, 1974.
15. Miller, K. S. and Ross, B., An Introduction to the Fractional Calculus and Differential Equations, Wiley, New York, 1993.
16. Padovan, J. and Zeid, I., 'Sub/superharmonic oscillations and the perturbation procedure', International Journal of Non-Linear Mechanics 16, 1981, 465-478.