Abstract
We discuss the propagation of transverse surface waves that are so-called whispering-gallery waves along a surface of an elastic cylinder with coating. The coating is modelled in the framework of linearized Gurtin–Murdoch surface elasticity. Other interpretations of the surface shear modulus are given and relations to so-called stiff interface and stiff skin model are discussed. The dispersion relations are obtained and analyzed.
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
no. 147,
ISSN: 0020-7225 - Language:
- English
- Publication year:
- 2020
- Bibliographic description:
- Eremeev V., Rosi G., Naili S.: Transverse surface waves on a cylindrical surface with coating// INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE -Vol. 147, (2020), s.103188-
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.ijengsci.2019.103188
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-
- In M. Abramowitz, & I. A. Stegun (Eds.), Handbook of mathematical functions: With formulas, graphs, and mathematical tables (10th). New York: Dover . Adamson, A. W. , & Gast, A. P. (1997). Physical chemistry of surfaces (6th). New York: Wiley . open in new tab
- Altenbach, H. , Eremeev, V. A. , & Morozov, N. F. (2010). On equations of the linear theory of shells with surface stresses taken into account. Mechanics of Solids, 45 (3), 331-342 . open in new tab
- Altenbach, H. , Eremeyev, V. A. , & Morozov, N. F. (2012). Surface viscoelasticity and effective properties of thin-walled structures at the nanoscale. Interna- tional Journal of Engineering Science, 59 , 83-89 . open in new tab
- Benveniste, Y. , & Miloh, T. (2001). Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials, 33 (6), 309-323 . open in new tab
- Benveniste, Y. , & Miloh, T. (2007). Soft neutral elastic inhomogeneities with membrane-type interface conditions. Journal of Elasticity, 88 (2), 87-111 . open in new tab
- Berdichevsky, V. L. (2010a). An asymptotic theory of sandwich plates. International Journal of Engineering Science, 48 (3), 383-404 . open in new tab
- Berdichevsky, V. L. (2010b). Nonlinear theory of hard-skin plates and shells. International Journal of Engineering Science, 48 (3), 357-369 . open in new tab
- Bhushan, B. (2017). Springer handbook of nanotechnology (4th). Berlin: Springer . open in new tab
- Chen, W. Q. , Wu, B. , Zhang, C. L. , & Zhang, C. (2014). On wave propagation in anisotropic elastic cylinders at nanoscale: Surface elasticity and its effect. Acta Mechanica, 225 (10), 2743-2760 . open in new tab
- Cuenot, S. , Frétigny, C. , Demoustier-Champagne, S. , & Nysten, B. (2004). Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Physical Review B, 69 (16), 165410 . open in new tab
- Duan, H. L. , Wang, J. , & Karihaloo, B. L. (2008). Theory of elasticity at the nanoscale. In Advances in applied mechanics: 42 (pp. 1-68). Elsevier . Eremeyev, V. A. (2016). On effective properties of materials at the nano-and microscales considering surface effects. Acta Mechanica, 227 (1), 29-42 .
- Eremeyev, V. A. , Cloud, M. J. , & Lebedev, L. P. (2018). Applications of tensor analysis in continuum mechanics . New Jersey: World Scientific . open in new tab
- Eremeyev, V. A. , Rosi, G. , & Naili, S. (2016). Surface/interfacial anti-plane waves in solids with surface energy. Mechanics Research Communications, 74 , 8-13 . open in new tab
- Eremeyev, V. A. , & Sharma, B. L. (2019). Anti-plane surface waves in media with surface structure: Discrete vs . continuum model. International Journal of Engineering Science, 143 , 33-38 . open in new tab
- Gorbushin, N. , Eremeyev, V. A. , & Mishuris, G. (2020). On stress singularity near the tip of a crack with surface stresses. International Journal of Engineering Science, 146 , 103183 . (in print). open in new tab
- Gurtin, M. E. , & Murdoch, A. I. (1975). A continuum theory of elastic material surfaces. Archive of Rationional Mechanics and Analysis, 57 (4), 291-323 . open in new tab
- Gurtin, M. E. , & Murdoch, A. I. (1978). Surface stress in solids. International Journal of Solids and Structures, 14 (6), 431-440 . open in new tab
- Huang, Z. (2018). Torsional wave and vibration subjected to constraint of surface elasticity. Acta Mechanica, 229 (3), 1171-1182 . open in new tab
- Huang, Z. , & Wang, J.-X. (2006). A theory of hyperelasticity of multi-phase media with surface/interface energy effect. Acta Mechanica, 182 (3-4), 195-210 . open in new tab
- Javili, A. , McBride, A. , & Steinmann, P. (2013). Thermomechanics of solids with lower-dimensional energetics: On the importance of surface, interface, and curve structures at the nanoscale. a unifying review. Applied Mechanics Reviews, 65 (1), 010802 . open in new tab
- Jing, G. Y. , Duan, H. , Sun, X. M. , Zhang, Z. S. , Xu, J. , Li, Y. D. , Wang, J. X. , & Yu, D. P. (2006). Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy. Physical Review B, 73 (23), 235409 . open in new tab
- Kim, C. I. , Ru, C. Q. , & Schiavone, P. (2013). A clarification of the role of crack-tip conditions in linear elasticity with surface effects. Mathematics and Mechanics of Solids, 18 (1), 59-66 . open in new tab
- Laplace, P. S. (1805). Sur l'action capillaire. In Supplément au livre X du traité de mécanique céleste: 4. Supplement 1, Livre X (pp. 771-777). Paris: Gauthier-Vil- lars et fils . open in new tab
- Laplace, P. S. (1806). Supplément à la théorie de l'action capillaire. In Traité de mécanique céleste: 4. Supplement 2, Livre X (pp. 909-945). Paris: Gauthier-Vil- lars et fils . open in new tab
- In W. R. Longley, & R. G. Van Name (Eds.), The collected works of J. Willard Gibbs, PHD., LL.d. : I Thermodynamics. New York: Longmans . open in new tab
- Miller, R. E. , & Shenoy, V. B. (20 0 0). Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11 (3), 139-147 . open in new tab
- Mishuris, G. , Öchsner, A. , & Kuhn, G. (2006a). FEM-analysis of nonclassical transmission conditions between elastic structures. Part 2: Stiff imperfect inter- face. CMC: Computers, Materials, & Continua,, 4 (3), 137-152 . open in new tab
- Mishuris, G. S. , Movchan, N. V. , & Movchan, A. B. (2006b). Steady-state motion of a Mode-III crack on imperfect interfaces. The Quarterly Journal of Mechanics & Applied Mathematics, 59 (4), 487-516 . open in new tab
- Mishuris, G. S. , Movchan, N. V. , & Movchan, A. B. (2010). Dynamic Mode-III interface crack in a bi-material strip. International Journal of Fracture, 166 (1-2), 121-133 . open in new tab
- Murdoch, A. I. (2005). Some fundamental aspects of surface modelling. Journal of Elasticity, 80 (1-3), 33-52 . open in new tab
- Orowan, E. (1970). Surface energy and surface tension in solids and liquids. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 316 (1527), 473-491 . open in new tab
- Rayleigh, L. (1910). CXII. The problem of the whispering gallery. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 20 (120), 1001-1004 . open in new tab
- Ru, C. Q. (2010). Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions. Science China Physics, Mechanics and Astronomy, 53 (3), 536-544 . open in new tab
- Rusanov, A. I. (2005). Surface thermodynamics revisited. Surface Science Reports, 58 (5-8), 111-239 . open in new tab
- Shenoy, V. B. (2005). Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Physical Review B, 71 (9), 094104 . Simmonds, J. G. (1994). A brief on tensor analysis (2nd). New York: Springer . open in new tab
- Strutt, J. W. (1945). The theory of sound. in two volumes . New York: Dover . open in new tab
- Vas'kova, V. , Viktorov, I. A. , Kaekina, T. , Maksimov, V. F. , Pyatakov, P. A. , & Talashev, A. A. (1974). Observation of transverse surface waves on a cylindrical surface of CdS crystal (In russian). Soviet Physics. Acoustics. (Akusticheskij Zhurnal), 23 (6), 861-866 .
- Victorov, I. A. (1974). Surface waves on cylindrical surfaces of crystals (in russian). Soviet Physics. Acoustics. (Akusticheskij Zhurnal), 20 (2), 199-206 . open in new tab
- Wang, J. , Huang, Z. , Duan, H. , Yu, S. , Feng, X. , Wang, G. , Zhang, W. , & Wang, T. (2011). Surface stress effect in mechanics of nanostructured materials. Acta Mechanica Solida Sinica, 24 , 52-82 . open in new tab
- Xu, L. , & Fan, H. (2016). Torsional waves in nanowires with surface elasticity effect. Acta Mechanica, 227 (6), 1783-1790 . open in new tab
- Xu, Q. , Jensen, K. E. , Boltyanskiy, R. , Sarfati, R. , Style, R. W. , & Dufresne, E. R. (2017). Direct measurement of strain-dependent solid surface stress. Nature Communications, 8 (1), 555 . Young, T. (1805). An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London, 95 , 65-87 . open in new tab
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