- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 652306, 22 pages
Fractal Geometry-Based Hypergeometric Time Series Solution to the Hereditary Thermal Creep Model for the Contact of Rough Surfaces Using the Kelvin-Voigt Medium
1Mechanical Engineering Department, The University of Jordan, Amman 11942, Jordan
2Computer Engineering Department, The University of Jordan, Amman 11942, Jordan
Received 28 January 2010; Accepted 23 May 2010
Academic Editor: Ming Li
Copyright © 2010 Osama M. Abuzeid et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- F. M. Borodich and D. A. Onishchenko, “Similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure,” International Journal of Solids and Structures, vol. 36, no. 17, pp. 2585–2612, 1999.
- J. A. Greenwood, “Problems with surface roughness,” in Fundamentals of Friction: Macroscopic and Microscopic Processes, I. L. Singer and H. M. Pollock, Eds., pp. 57–76, Kluwer, Boston, Mass, USA, 1992.
- A. Majumdar and B. Bhushan, “Role of fractal geometry in roughness characterization and contact mechanics of surfaces,” Journal of Tribology, vol. 112, no. 2, pp. 205–216, 1990.
- B. B. Mandelbrot, D. E. Passoja, and A. J. Paullay, “Fractal character of fracture surfaces of metals,” Nature, vol. 308, no. 5961, pp. 721–722, 1984.
- M. Li and W. Zhao, “Representation of a stochastic traffic bound,” to appear in IEEE Transactions on Parallel and Distributed Systems, IEEE Computer Society Digital Library, IEEE Computer Society, http://doi.ieeecomputersociety. org/10.1109/TPDS.2009.162.
- M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584–2594, 2008.
- M. Li, “Generation of teletraffic of generalized Cauchy type,” Physica Scripta, vol. 82, no. 2, Article ID 025007, 2010.
- K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, UK, 1985.
- J. A. Greenwood and J. B. P. Williamson, “Contact of nominally flat surfaces,” Proceedings of the Royal Society of London. Series A, vol. 295, no. 1442, pp. 300–319, 1966.
- A. Majumdar and B. Bhushan, “Fractal model of elastic-plastic contact between rough surfaces,” Journal of Tribology, vol. 113, pp. 1–11, 1991.
- F. M. Borodich and A. B. Mosolov, “Fractal roughness in contact problems,” Journal of Applied Mathematics and Mechanics, vol. 56, no. 5, pp. 786–795, 1992.
- T. L. Warren and D. Krajcinovic, “Fractal models of elastic-perfectly plastic contact of rough surfaces based on the Cantor set,” International Journal of Solids and Structures, vol. 32, no. 19, pp. 2907–2922, 1995.
- T. L. Warren, A. Majumdar, and D. Krajcinovic, “A fractal model for the rigid-perfectly plastic contact of rough surfaces,” Journal of Applied Mechanics, vol. 63, no. 1, pp. 47–54, 1996.
- O. Abuzeid, “Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: Maxwell type medium,” Dirasat-Engineering Sciences, The University of Jordan, vol. 30, no. 1, pp. 22–36, 2003.
- O. M. Abuzeid and P. Eberhard, “Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: standard linear solid (SLS) material,” Journal of Tribology, vol. 129, no. 3, pp. 461–466, 2007.
- O. M. Abuzeid and T. A. Alabed, “Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium,” Tribology International, vol. 42, no. 2, pp. 206–212, 2009.
- F. Borodich, “Fractals and surface roughness in EHL,” in IUTAM Symposium on Elastohydrodynamics and Micro-Elastohydrodynamics, R. Snidle and H. Evans, Eds., vol. 134 of Solid Mechanics and Its Applications, pp. 397–408, Springer, Dordrecht, The Netherlands, 2006.
- B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, Calif, USA, 1982.
- R. D. Mauldin and S. C. Williams, “On the Hausdorff dimension of some graphs,” Transactions of the American Mathematical Society, vol. 298, no. 2, pp. 793–803, 1986.
- D. Wójcik, I. Białynicki-Birula, and K. Zyczkowski, “Time evolution of quantum fractals,” Physical Review Letters, vol. 85, no. 24, pp. 5022–5025, 2000.
- A. N. Al-Rabadi, Reversible Logic Synthesis: From Fundamentals to Quantum Computing, Springer, Berlin, Germany, 2004.
- C. Cattani and A. Kudreyko, “Application of periodized harmonic wavelets towards solution of eigenvalue problems for integral equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 570136, 8 pages, 2010.
- E. G. Bakhoum and C. Toma, “Dynamical aspects of macroscopic and quantum transitions due to coherence function and time series events,” Mathematical Problems in Engineering, vol. 2010, Article ID 428903, 13 pages, 2010.
- G. Toma, “Specific differential equations for generating pulse sequences,” Mathematical Problems in Engineering, vol. 2010, Article ID 324818, 11 pages, 2010.
- G. Mattioli, M. Scalia, and C. Cattani, “Analysis of large amplitude pulses in short time intervals: application to neuron interactions,” Mathematical Problems in Engineering, vol. 2010, Article ID 895785, 15 pages, 2010.
- S. Y. Chen, Y. F. Li, and J. Zhang, “Vision processing for realtime 3-D data acquisition based on coded structured light,” IEEE Transactions on Image Processing, vol. 17, no. 2, pp. 167–176, 2008.
- S. Y. Chen, Y. F. Li, Q. Guan, and G. Xiao, “Real-time three-dimensional surface measurement by color encoded light projection,” Applied Physics Letters, vol. 89, no. 11, Article ID 111108, 2006.
- K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, Chichester, UK, 1990.
- P. S. Modenov and A. S. Parkhomenko, Geometric Transformations. Vol. 1: Euclidean and Affine Transformations, Academic Press, New York, NY, USA, 1965.
- R. F. Voss, “Random fractal forgeries,” in Fundamental Algorithms in Computer Graphics, R. A. Earnshaw, Ed., pp. 805–835, Springer, Berlin, Germany, 1985.
- A. Majumdar and C. L. Tien, “Fractal characterization and simulation of rough surfaces,” Wear, vol. 136, no. 2, pp. 313–327, 1990.
- J. Lopez, G. Hansali, H. Zahouani, J. C. Le Bosse, and T. Mathia, “3D fractal-based characterisation for engineered surface topography,” International Journal of Machine Tools and Manufacture, vol. 35, no. 2, pp. 211–217, 1995.
- M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010.
- M. Li and J.-Y. Li, “On the predictability of long-range dependent series,” Mathematical Problems in Engineering, vol. 2010, Article ID 397454, 9 pages, 2010.
- R. S. Sayles and T. R. Thomas, “Surface topography as a nonstationary random process,” Nature, vol. 271, no. 5644, pp. 431–434, 1978.
- S. R. Brown, “Simple mathematical model of a rough fracture,” Journal of Geophysical Research, vol. 100, no. 4, pp. 5941–5952, 1995.
- M. V. Berry and Z. V. Lewis, “On the Weierstrass-Mandelbrot fractal function,” Proceedings of the Royal Society of London. Series A, vol. 370, no. 1743, pp. 459–484, 1980.
- E. H. Lee and J. R. M. Radok, “The contact problem for viscoelastic bodies,” Journal of Applied Mechanics, vol. 27, pp. 438–444, 1960.
- T. C. T. Ting, “The contact stress between a rigid indenter and a viscoelastic half-space,” Journal of Applied Mechanics, vol. 33, pp. 845–854, 1966.
- T. C. T. Ting, “Contact problems in the linear theory of viscoelasticity,” Journal of Applied Mechanics, vol. 35, pp. 248–254, 1968.
- G. R. Nghieh, H. Rahnejat, and Z. M. Jin, “Contact mechanics of viscoelastic layered surface,” in Contact Mechanics III, M. H. Aliabadi and A. Samartin, Eds., pp. 59–68, Computational Mechanics Publications, Boston, Mass, USA, 1997.
- K. J. Wahl, S. V. Stepnowski, and W. N. Unertl, “Viscoelastic effects in nanometer-scale contacts under shear,” Tribology Letters, vol. 5, no. 1, pp. 103–107, 1998.
- D. J. Whitehouse and J. F. Archard, “The properties of random surfaces of significance in their contact,” Proceedings of the Royal Society of London. Series A, vol. 316, pp. 97–121, 1970.
- J. R. M. Radok, “Visco-elastic stress analysis,” Quarterly of Applied Mathematics, vol. 15, pp. 198–202, 1957.
- P. E. D'yachenko, N. N. Tolkacheva, G. A. Andreev, and T. M. Karpova, The Actual Contact Area between Touching Surfaces, Consultant Bureau, New York, NY, USA, 1964.
- N. J. Distefano and K. S. Pister, “On the identification problem for thermorheologically simple materials,” Acta Mechanica, vol. 13, no. 3-4, pp. 179–190, 1972.
- T. Junisbekov, V. Kestelman, and N. Malinin, Stress Relaxation in Viscoelastic Materials, Science Publishers, Enfield, NH, USA, 2nd edition, 2003.
- W.-S. Lee and C.-Y. Liu, “The effects of temperature and strain rate on the dynamic flow behaviour of different steels,” Materials Science and Engineering A, vol. 426, no. 1-2, pp. 101–113, 2006.
- J. Boyle and J. Spencer, Stress Analysis for Creep, Butterworths-Heinemann, London, UK, 1st edition, 1983.
- I. H. Shames and F. A. Cozzarelli, Elastic and Inelastic Stress Analysis, Prentice-Hall International, Englewood Cliffs, NJ, USA, 1992.
- G. E. Roberts and H. Kaufman, Table of Laplace Transforms, W. B. Saunders, Philadelphia, Pa, USA, 1966.
- L. J. Slater, Confluent Hypergeometric Functions, Cambridge University Press, New York, NY, USA, 1960.
- W. Nowacki, Thermoelasticity, Pergamon Press, Oxford, UK, 2nd edition, 1986.
- Z. Handzel-Powierza, T. Klimczak, and A. Polijaniuk, “On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces,” Wear, vol. 154, no. 1, pp. 115–124, 1992.