Application of fractional derivatives in thermal analysis of disk brakes

Nonlinear Dynamics

Volumn 38, Issue 1-4, 2004, Pages 191-206

  Agrawal, Om Prakash ^a  

^a SOUTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Fractional derivatives; Fractional power polynomials; Thermal analysis of disk brakes

Indexed keywords

COMPUTER PROGRAMMING; DISKS (MACHINE COMPONENTS); ELASTIC MODULI; ERROR ANALYSIS; FRICTION; HEAT FLUX; HEAT LOSSES; LEAST SQUARES APPROXIMATIONS; POLYNOMIALS; STATISTICAL METHODS; THERMAL EFFECTS;

FRACTIONAL DERIVATIVES; FRACTIONAL POWER POLYNOMIALS; SURFACE TEMPERATURE; THERMAL ANALYSIS OF DISK BRAKES;

BRAKES;

EID: 15544379440     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-004-3755-7     Document Type: Conference Paper

References (19)

1. Du, S. 'Thermoelastic Effects in Automotive Brakes', Ph.D. Thesis, Mechanical Engineering, University of Michigan, Ann Arbor, 1997.
2. Du, S., Zagrodzki, P., Barber, J. R., and Hulbert, G. M. 'Finite element analysis of frictionally excited thermoelastic instability', Journal of Thermal Stresses 20, 1997, 185-201.
3. Agrawal, O. P. 'Fractional derivatives and its applicationin thermal analysis and properties measurements of disk brakes', Quarterly Report, Center for Advanced Friction Studies, SIUC, May 2003.
4. Samko, S. G., Kilbas, A. A., and Marichev, O. I. Fractional Integrals and Derivatives - Theory and Applications, Gordon and Breach, Longhorne, Pennsylvania, 1993.
5. Oldham, K. B. and Spanier, J. The Fractional Calculus, Academic Press, New York, 1974.
6. Miller, K. S. and Ross, B. An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
7. Gorenflo, R. and Mainardi, F. 'Fractional calculus: Integral and differential equations of fractional order', in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi (eds.), Springer-Verlag, Vienna, 1997, pp. 223-276.
8. Mainardi, F. 'Fractional calculus: Some basic problems in continuum and statistical mechanics', in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi (eds.), Springer-Verlag, Vienna, 1997, pp. 291-348.
9. Rossikhin, Y. A. and Shitikova, M. V. 'Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids', Applied Mechanics Reviews 50, 1997, 15-67.
10. Podlubny, I. Fractional Differential Equations, Academic Press, New York, 1999.
11. Butzer, P. L. and Westphal, U. 'An introduction tofractional calculus', in Applications of Fractional Calculus in Physics, R. Hilfer (ed.), World Scientific, River Edge, New Jersey, 2000, 1-85.
12. Kulish, V. V. and Lage, J. L. 'Fractional diffusion solutions for transient local temperature and heat-flux', ASME Journal of Heat Transfer 122, 2000, 372-377.
13. Kulish, V. V., Lage, J. L., Komarov, P. L., and Raad, P. E. 'A fractional-diffusion theory for calculating thermal propertiesof thin films from surface transient thermoreflectance measurements', ASME Journal of Heat Transfer 123, 2001, 1133-1138.
14. Battaglia, J. L., Cois, O., Puigsegur, L., Oustaloup, A. 'Solving an inverse heat conduction problem using a non-integer identified model', International Journal of Heat and Mass Transfer 44, 2001, 2671-2680.
15. Carslaw, H. S. and Jaeger, J. C. Conduction of Heat In Solids, Oxford University Press, Oxford, 1959.
16. Reddy, J. N. and Gartling, D. K. The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC Press, New York, 2001.
17. Beck, J. V., Blackwell, B., and St. Clair, Jr., C. R. Inverse Heat Conduction: Ill-Posed Problems, Wiley, New York, 1985.
18. Wriggers, P. and Miehe, C. 'Contact constraints within coupled thermomechanical analysis - A finite element model', Computer Methods in Applied Mechanics and Engineering 113, 1994, 301-319.
19. Marx, D.T., Policandriotes, T., Zhang, S., Scott, J., Dinwiddie, R. B., and Wang, H. 'Measurement of interfacial temperaturesduring testing of a subscale aircraft brake', Journal of Physics D: Applied Physics 34, 2001, 976-984.