Share This Article:

On the Damped Beams with Hysteresis

Abstract Full-Text HTML Download Download as PDF (Size:2262KB) PP. 6-14
DOI: 10.4236/wjm.2011.11002    4,408 Downloads   9,563 Views   Citations

ABSTRACT

This paper discusses the hysteretic behavior of beams with external elements made from auxetic materials. The damping force is modeled by using the nonlocal theory. Unlike the local models, the damping force is modeled as a weighted average of the velocity field over the temporal and spatial domains, determined by a kernel function based on distance measures. The hysteresis operator is continuous and it is defined in con-nection with the Euler-Bernoulli equation. The problem is solved by reducing it to a system of differential inclusions.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Poienariu, M. Ionescu, I. Girip, L. Munteanu and V. Chiroiu, "On the Damped Beams with Hysteresis," World Journal of Mechanics, Vol. 1 No. 1, 2011, pp. 6-14. doi: 10.4236/wjm.2011.11002.

References

[1] K. E. Evans, M. A. Nkansah, I. J. Hutchinson and S. C. Rogers, “Molecular Network Design,” Nature, Vol. 353, 1991, pp. 124-125. doi:10.1038/353124a0
[2] R. S. Lakes, “Experimental Microelasticity of Two Porous Solids,” International Journal of Solids and Structures, Vol. 22, No. 1, 1986, pp. 55-63. doi:10.1016/0020- 7683(86)90103-4
[3] R. S. Lakes, “Foam Structures with a Negative Poisson’s Ratio,” Science, Vol. 235, 1987, pp. 1038-1040. doi:10. 1126/science.235.4792.1038
[4] R. S. Lakes, “Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua,” Journal of Engineering Materials and Technology, Vol. 113, No. 1, 1991, pp. 148-155. doi:10.1115/1.2903371
[5] D. W. Overaker, L. M. Cuiti?o and N. A. Langrana, “Effects of Morphology and Orientation on the Behavior of Two-Dimensional Hexagonal Foams and Application in a Re-Entrant Foam Anchor Model,” Mechanics of Materials, Vol. 29, No. 1, June 1998, pp. 43-52. doi:10.1016/ S0167-6636(98)00004-0
[6] Y.-C. Wang and R. Lakes, “Analytical Parametric Analysis of the Contact Problem of Human Buttocks and Negative Poisson’s Ratio Foam Cushions,” International Journal of Solids and Structures, Vol. 39, No. 18, September 2003, pp. 4825-4838. doi:10.1016/S0020-7683 (02)00379-7
[7] A. E. H. Love, “A Treatise on the Mathematical Theory of Elasticity,” Dover, 4th Edition, New York, 1926.
[8] D. J. Gunton and G. A. Saunders, “Stability Limits on the Poisson Ratio,” Journal of Material Science, Vol. 7, 1972, pp. 1061-1068. doi:10.1007/BF00550070
[9] Y. Li, “The Anisotropic Behavior of Poisson’s Ratio, Young’s Modulus, and Shear Modulus in Hexagonal Materials,” Physica Status Solidi A, Vol. 38, No. 1, November 1976, pp. 171-175. doi:10.1002/pssa.2210380119
[10] R. H. Baughman, J. M. Shacklette, A. A. Zakhidov and S. Stafstrom, “Negative Poisson’s Ratios as a Common Feature of Cubic Metals,” Nature, Vol. 392, 1998, pp. 362-365. doi:10.1038/32842
[11] F. Scarpa, J. A. Giacomin, A. Bezazi and W. A. Bullough, “Dynamic Behaviour and Damping Capacity of Auxetic Foam Pads,” SPIE Proceeding, 2006.
[12] ?. Donescu, V. Chiroiu amd L. Munteanu, “On the Young’s Modulus of a Auxetic Composite Structure,” Mechanics Research Communications, Vol. 36, No. 3, 2009, pp. 294-301. doi:10.1016/j.mechrescom.2008.10.0 06
[13] ?. Donescu, L. Munteanu, P. P. Delsanto and V. Mo?negu?u, “On the Advanced Auxetic Composites,” Research Trends in Mechanics, Vol. 3, 2009, pp. 78-93.
[14] Y. Lei, M. I. Friswell and S. Adhikari, “A Galerkin Method for Distributed Systems with Nonlocal Damp- ing,” International Journal of Solids and Structures, Vol. 43, No. 11-12, June 2006, pp. 3381-3400. doi:10.1016/j. ijsolstr.2005.06.058
[15] M. I. Friswell, S. Adhikari and Y. Lei, “Non-Local Finite Element Analysis of Damped Beams,” International Journal of Solids and Structures, Vol. 44, No. 22-23, 2007, pp. 7564-7576. doi:10.1016/j.ijsolstr.2007.04.023
[16] M. I Friswell, S. Adhikari and Y. Lei, “Vibration Analysis of Beams with Non-Local Foundations Using the Finite Element Method,” International Journal of Numerical Methods in Engineering, Vol. 71, No. 11, 2007, pp. 1365-1386. doi:10.1002/nme.2003
[17] W. Flugge,“Viscoelasticity,” 2nd Editon, Springer-Verlag, Berlin, 1975.
[18] F. Scarpa, P. Pastorino, A. Garelli, S. Patsias and M. Ruzzene, “Auxetic Compliant Flexible PU Foams: Static and Dynamic Properties,” Physica Status Solidi B, Vol. 242, No. 3, 2005, pp. 681-694. doi:10.1002/pssb.200460 386
[19] L. Munteanu, D. Dumitriu, ?. Donescu and V. Chiroiu, “On the Complexity of the Auxetic Systems,” Proceed- ings of the European Computing Conference, Vol. 2, 2009, pp. 631-636.
[20] V. Chiroiu, St. Donescu, L. Munteanu and V. Mo?negu?u, “The Dynamics of Beams with Auxetic Patches,” Proceedings of the International Conference on Advanced Materials for Application in Acoustics and Vibration AMAAV’09, Cairo, January 2009.
[21] V. Chiroiu, L. Munteanu and St. Donescu, “On the Beams with External Auxetic Patches,” Advances in Mechanical Engineering, 2009, pp. 1-10. doi:10.1155/2009/ 430379
[22] L. Munteanu, V. Chiroiu, D. Dumitriu, D. Baldovin, St. Donescu and C. Chiroiu, “On the Eigenvalues Optimization of Euler-Bernoulli Beams with Nonlocal Damping Pathes,” Révue Roumaine des Sciences Techniques, série de Mécanique Appliquée, Vol. 54, No. 1, 2009, pp. 53-66.
[23] L. Munteanu, V. Chiroiu and P. P. Teodorescu, “Nano- beams with Damping Elements,” In: M. Zaharescu, M. Ciurea, I. Kleps, D. Dascalu, Eds., Series in Micro and Nanoengineering – Nanostructuring and Nanocharacterization, Vol. 16, 2010, pp. 241-256.
[24] L. Munteanu, P. P. Delsanto, D. Dumitriu and V. Mosnegutu, “On the Characterization of Auxetic Materi- als,” In: D. Popa, V. Chiroiu, I. Toma, Eds, Research Trends in Mechanics, Vol. 2, 2008, pp. 205-234.
[25] L. Munteanu, V. Chiroiu, D. Dumitriu and M. Beldiman, “On the Characterization of Auxetic Composites,” Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science, Vol. 9, No. 1, 2008, pp. 33-40.
[26] V. Chiroiu, L. Munteanu, D. Dumitriu, M. Beldiman and C. Secara, “On the Arhitecture of a New Cellular Elastic Material,” Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science, Vol. 9, No. 2, 2008, pp. 105-115.
[27] L. Munteanu, V. Chiroiu, T. Sireteanu and L. Tenek, “Vibrations of a Micropaddle with Periodic Auxetic Core,” Révue Roumaine des Sciences Techniques, série de Mécanique Appliquée, Vol. 55, No. 2, 2010, pp. 101- 114.
[28] M. Beldiman, L. Munteanu and M. Poienariu, “On the Multifunctional Nanofoils Based on Carbon Nanotubes and Auxetic Foams,” In: L. Munteanu, V. Chiroiu, T. Sireteanu, Eds., Research Trends in Mechanics, Vol. 4, 2010, pp. 9-24.
[29] A. Visintin, “Hysteresis and Semigroups,” In: A. Visintin, Ed., Models of Hysteresis, Longman, Harlow, 1993, pp. 192-206.
[30] A. Visintin, “Differential Models of Hysteresis,” Springer- Verlag, Berlin, 1995.
[31] A. Visintin, “Quasi-Linear Hyperbolic Equations with Hysteresis,” Annales de l’ Institut Henri Poincaré, Non- linear Analysis, Vol. 19, No. 4, 2002, pp. 451-476.
[32] Y. Kōmura, “Nonlinear Semi-Groups in Hilbert Space,” Journal of the Mathematical Society of Japan, Vol. 19, No. 4, 1967, pp. 493-507. doi:10.2969/jmsj/01940493
[33] J. Kopfová, “Nonlinear Semigroup Methods in Problems with Hysteresis,” Discrete and Continuous Dynamical Systems Supplement, pp. 580-589, 2007
[34] M. C. Crandall and T. M. Liggett, “Generation of Semigroups of Nonlinear Transformations on General Banach Spaces,” American Journal of Mathematics, Vol. 93, No. 2, April 1971, pp. 265-298. doi:10.2307/2373376
[35] V. Barbu, “Nonlinear Semigroups and Differential Equations in Banach Spaces,” Noordhoff, Leyden, 1976.
[36] A. Bezazi and F. Scarpa, “Mechanical Behaviour of Conventional and Negative Poisson’s Ratio Thermoplastic Polyurethane Foams under Compressive Cyclic Loading,” International Journal of Fatigue, Vol. 29, No. 5, 2007, pp. 922-930. doi:10.1016/j.ijfatigue.2006.07.015
[37] F. Scarpa, J. A. Giacomin, A. Bezazi and W. A. Bullough, “Dynamic Behaviour and Damping Capacity of Auxetic Foam Pads,” SPIE Proceedings of Smart Structures and Materials, 2006.
[38] V. Preda, M. F. Ionescu, V. Chiroiu and T. Sireteanu, “A Preisach Model for the Analysis of the Hysteretic Phenomena,” Révue Roumaine des Sciences Techniques, série de Mécanique Appliquée, Vol. 55, No. 3, 2010, pp. 75-86.
[39] A. E. Charalampakis and V. K. Koumousis, “A Bouc- Wen Model Compatible with Plasticity Postulates,” Jour- nal of Sound and Vibration, Vol. 322, 2009, pp. 954-968, doi:10.1016/j.jsv.2008.11.017

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.