On the application to robotics of the Euler-Bernoulli beams with external patches
Keywords:
Beam with external patches, nonlocal theory, optimization, dampingAbstract
The paper discusses the behavior of a Euler-Bernoulli beam with external patches made from GeSbTe chalcogenide material. The nonlocal theory is used to model the damping force as a weighted average of the velocity field over a suitable distance. The resonance is avoided through a careful choosing of the patch location and the eigenvalues. The atomic-level knowledge of the material gives the route for understanding their properties necessary to specific devices.
References
CHIROIU, V., MUNTEANU, L., DONESCU, S., On the beams with external auxetic patches, Advances in Mechanical Engineerings, 1, SAGE Journals, 2009, 10.1155/2009/430379.
LAKES, R. S., Experimental Microelasticity of Two Porous Solids, Int. J. Solids, Structures, 22, 1, pp. 55-63, 1986.
LAKES, R. S., Foam structures with a negative Poisson's ratio, Science, 235, 4792, pp. 1038-1040, 1987.
LAKES, R. S., Experimental micro mechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua, J. Engineering Materials and Technology, 113, 1, pp. 148-155, 1991.
OVERAKER, D.W., CUITINO, L.M., LANGRANA, N.A., Effects of morphology and orientation on the behavior of two-dimensional hexagonal foams and application in a re-entrant foam anchor model, Mech. Mater., 29, 1, pp. 43-52,1998.
WANG, Y.-C., LAKES, R., Analytical parametric analysis of the contact problem of human buttocks and negative Poisson’s ratio foam cushions, Int. J. Solids Structures, 39, 18, pp. 4825-4838, 2002.
LOVE, A. E. H., A treatise on the mathematical theory of elasticity, 4th ed., Dover, New York, 1926.
GUNTON, D.J., SAUNDERS, G.A., Stability Limits on the Poisson Ratio, J. Mater. Sci., 7, .pp. 1061-1068, 1972.
LI, Y., The anisotropic behavior of Poisson's ratio, Young's modulus, and shear modulus in hexagonal materials, Phys. Status Solidi, 38, 1, pp. 171-175, 1976.
BAUGHMAN, R.H., SHACKLETTE, J.M., ZAKHIDOV, A.A., STAFSTROM, S., Negative Poisson’s ratios as a common feature of cubic metals, Nature, 392, pp. 362-365, 1998.
SCARPA, F., GIACOMIN, J.A., BEZAZI, A., BULLOUGH, W.A., Dynamic behaviour and damping capacity of auxetic foam pads, SPIE Proceeding, 6169, Smart Structures and Materials 2006: Damping and Isolation, William W. Clark, Mehdi Ahmadian, Arnold Lumsdaine, Editors, 61690T, 2006.
DONESCU, S., CHIROIU, V., MUNTEANU, L., On the Young’s modulus of a auxetic composite structure, Mechanics Research Communications, 36, 3, pp. 294-301, 2009.
DONESCU, S., MUNTEANU, L., DELSANTO, P.P., MOSNEGUTU,V., Ch.4: On the advanced auxetic composites, Research Trends in Mechanics, 3, Ed. Academiei, 2009.
CHIROIU, V., DONESCU, S., MUNTEANU, L., MOSNEGUTU, V., The dynamics of beams with auxetic patches, Proceedings of the International Conference on Advanced Materials for Application in Acoustics and Vibration AMAAV’09, The British University of Egypt, 4-6 January, Cairo, 2009.
MUNTEANU, L., DUMITRU, D., DONESCU, S., CHIROIU, V., On the complexity of the auxetic systems, part VIII, ch. 65, Proceedings of the European Computing Conference, Lecture Notes in Electrical Engineering 28, 2 (eds. N.Mastorakis, V.Mladenov), Springer-Verlag, pp. 631-636, 2009.
SCARPA, F., PASTORINO, P., GARELLI, A., PATSIAS, S., RUZZENE, M., Auxetic Compliant Flexible PU Foams: Static and Dynamic Properties, Physica Status Solidi B, 242, 3, pp. 681-694, 2005.
FRISWELL, M. I, ADHIKARI, S., LEI, Y., Non-local finite element analysis of damped beams, International Journal of Solids and Structures, 44, 22-23, pp. 7564-7576, 2007.
FRISWELL, M. I, ADHIKARI, S., LEI, Y., Vibration analysis of beams with non-local foundations using the finite element method, International Journal of Numerical Methods in Engineering, 71, 11, pp. 1365-1386, 2007.
FLUGGE, W., Viscoelasticity, 2nd ed. Springer-Verlag, Berlin, 1975.
LEI, Y., FRISWELL, M.I., ADHIKARI, S., A Galerkin method for distributed systems with nonlocal damping, International Journal of Solids and Structures, 43, pp. 3381-3400, 2006.
GHONEIM, H., Fluid surface damping versus constrained layer damping for vibration suppression of simply supported beams, Smart Materials and Structures, 6, pp. 40-46, 1997.
ADHIKARI, S., Dynamics of non-viscously damped linear systems, ASCE Journal of Engineering Mechanics, 128, 3, pp. 328-339, 2002.
ADHIKARI, S., LEI, Y., FRISWELL, M. I., Modal analysis of non-viscously damped beams, Transactions of ASME, Journal of Applied Mechanics, 74, 5, pp. 1026-1030, 2007.
WAGNER, N., ADHIKARI, S., Symmetric state-space formulation for a class of non-viscously damped systems, AIAA Journal, 41, 5,pp. 951-956, 2003.
BANKS, H.T., INMAN, D.J., On damping mechanisms in beams, Journal of Applied Mechanics, 58, 3, pp. 716-723, 1991.
BANKS, H.T., WANG, Y. INMAN, D.J., Bending and shear damping in beams-frequency-domain estimation techniques, Journal of Vibration and Acoustics, 116, 2, pp. 188-197, 1994.
SORRENTINO, S., MARCHESIELLO, S., PIOMBO, B.A.D., A new analytical technique for vibration analysis of non-proportionally damped beams, Journal of Sound and Vibration, 265, 4, pp. 765-782, 2003.
BEZAZI, A., SCARPA, F., Mechanical behaviour of conventional and negative Poisson's ratio thermoplastic polyurethane foams under compressive cyclic loading, International Journal of Fatigue, 29, 5, pp. 922-930, 2007.
CHIROIU, V., On the eigenvalues optimization of beams with damping patches, New Aspects of Engineering Mechanics Structures, Geology, Mathematics and Computers in Science Engineering, A Series of Reference Books and Textbooks, (EMESEG '09) Heraklion, WSEAS Press, pp. 117-122, 2008.
MUNTEANU, L., DONESCU, S., Introduction to Soliton Theory: Applications to Mechanics, Book Series “Fundamental Theories of Physics”, 143, Kluwer Academic Publishers, 2004.
CHIROIU, V., CHIROIU, C., Probleme inverse in mecanica (Inverse problems in mechanics), Ed. Academiei, Bucharest, 2003.
BENDSOE, M..P., OLHOFF, N., TAYLOR, J.E., A variational formulation for multicriteria structural optimization, Journal of Structural Mechanics, 11, 4, pp. 523-544, 1983.
PEDERSEN, N.L., Designing plates for minimum internal resonance, Struct. Multidisc. Optim., 28, 1, pp. 1-10, 2004.
PEDERSEN, N.L., Optimization of holes in plates for control of eigenfrequencies, Struct. Multidisc. Optim., 30, 4, pp. 297-307, 2005.
PEDERSEN, N.L., On simultaneous shape and orientational design for eigenfrequency optimisation, Danish Center for Applied Mathematics and Mechanics, report nr.714, 2006.
Published
Issue
Section
Copyright (c) 2023 The Romanian Journal of Technical Sciences. Applied Mechanics.
This work is licensed under a Creative Commons Attribution 4.0 International License.