RUS  ENG
Full version
JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics

Izv. Saratov Univ. Math. Mech. Inform., 2024, Volume 24, Issue 1, Pages 86–96 (Mi isu1011)

On the influence of surface stresses and inertia on the natural low-frequency vibrations of an elastic ultrathin strip-beam
G. I. Mikhasev, N. D. Le

References

1. Lavrik N. V., Sepaniak M. J., Datskos P. G., “Cantilever transducers as a platform for chemical and biological sensors”, Review of Scientific Instruments, 75 (2004), 2229–2253  crossref
2. Zhang Y., Khan M., Huang Y., Ryou J., Deotare P., Dupuis R., Lonċar M., “Photonic crystal nanobeam lasers”, Applied Physics Letters, 97:5 (2010), 051104  crossref
3. Qiao Q., Xia J., Lee C., Zhou G., “Applications of photonic crystal nanobeam cavities for sensing”, Micromachines, 9:11 (2018), 541  crossref
4. Cuenot S., Fretigny C., Demoustier-Champagne S., Nysten B., “Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy”, Physical Review. B, 69:16 (2004), 165410–165415  crossref
5. Sun C. T., Zhang H., “Size-dependent elastic moduli of platelike nanomaterials”, Journal of Applied Physics, 93 (2003), 1212–1218  crossref
6. Zhang H., Sun C. T., “Nanoplate model for platelike nanomaterials”, AIAA Journal, 42:10 (2004), 2002–2009  crossref  mathscinet
7. Zhou L. G., Huang H., Are surfaces elastically softer or stiffer?, Applied Physics Letters, 84:11 (2004), 1940–1942  crossref
8. Gurtin M. E., Murdoch A. I., “Surface stress in solids”, International Journal of Solids and Structures, 14:6 (1978), 431–440  crossref  zmath
9. Wang J., Huang Z., Duan H., Yu S., Feng X., Wang G., Zhang W., Wang T., “Surface stress effect in mechanics of nanostructured materials”, Acta Mechanica Solida Sinica, 24:1 (2011), 52–82  crossref  mathscinet
10. Achenbach J., Wave Propagation in Elastic Solids, North Holland, Amsterdam, The Netherland, 1973, 440 pp.  mathscinet  zmath
11. Eremeyev V. A., Rosi G., Naili S., “Surface/interfacial anti-plane waves in solids with surface energy”, Mechanics Research Communications, 74 (2016), 8–13  crossref
12. Zhu F., Pan E., Qian Z., Wang Y., “Dispersion curves, mode shapes, stresses and energies of SH and Lamb waves in layered elastic nanoplates with surface/interface effect”, International Journal of Engineering Science, 142 (2019), 170–184  crossref  mathscinet
13. Mikhasev G. I., Botogova M. G., Eremeyev V. A., “Anti-plane waves in an elastic thin strip with surface energy”, Philosophical Transactions of the Royal Society, Series A: Mathematical, Physical and Engineering Sciences, 380:2231 (2022), 20210373  crossref  mathscinet
14. Mikhasev G. I., Erbas B., Eremeyev V. A., “Anti-plane shear waves in an elastic strip rigidly attached to an elastic half-space”, International Journal of Engineering Science, 184 (2023), 103809  crossref  mathscinet
15. Mogilevskaya S. G., Zemlyanova A. Y., Kushch V. I., “Fiber- and particle-reinforced composite materials with the Gurtin – Murdoch and Steigmann – Ogden surface energy endowed interfaces”, Applied Mechanics Reviews, 73 (2021), 1–18  crossref
16. Gorbushin N., Eremeyev V. A., Mishuris G., “On stress singularity near the tip of a crack with surface stresses”, International Journal of Engineering Science, 146 (2020), 103183  crossref  mathscinet  zmath
17. Lim C. W., He L. H., “Size-dependent nonlinear response of thin elastic films with nano-scale thickness”, International Journal of Mechanical Science, 46 (2004), 1715–1726  crossref  zmath
18. Lu P., He L. H., Lee H. P., Lu C., “Thin plate theory including surface effects”, International Journal of Solids and Structures, 43 (2006), 4631–4647  crossref  zmath
19. Lu L., Guoa X., Zhao J., “On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy”, International Journal of Engineering Science, 124 (2018), 24–40  crossref  mathscinet
20. Zhou J., Lu P., Xue Y., Lu C., “A third-order plate model with surface effect based on the Gurtin – Murdoch surface elasticity”, Thin-Walled Structures, 185 (2023), 110606  crossref
21. Yang W., Wang S., Kang W., Yu T., Li Y., “A unified high-order model for size-dependent vibration of nanobeam based on nonlocal strain/stress gradient elasticity with surface effect”, International Journal of Engineering Science, 182 (2023), 103785  crossref  mathscinet
22. Altenbach H., Eremeyev V. A., “On the shell theory on the nanoscale with surface stresses”, International Journal of Engineering Science, 49:12 (2011), 1294–1301  crossref  mathscinet  zmath
23. Altenbach H., Eremeyev V. A., Morozov N. F., “Surface viscoelasticity and effective properties of thin-walled structures at the nanoscale”, International Journal of Engineering Science, 59 (2012), 83–89  crossref  mathscinet  zmath
24. Tovstik P. E., Tovstik T. P., “Generalized Timoshenko – Reissner models for beams and plates, strongly heterogeneous in the thickness direction”, ZAMM – Journal of Applied Mathematics and Mechanics, 97:3 (2017), 296–308  crossref  mathscinet
25. Mikhasev G., Botogova M., Le N., “Flexural deformations and vibrations of a three-layer beam-strip with a stiff core and soft skins”, Progress in Continuum Mechanics, Advanced Structural Materials, 196, eds. H. Altenbach, H. Irschik, A. Porubov, Springer, Cham, 2023, 265–282  crossref
26. Kaplunov J., Kossovitch L., Nolde E., Dynamics of Thin Walled Elastic Bodies, Academic Press, San Diego, 1998, 226 pp.  mathscinet  zmath
27. Timoshenko S., “On the correction for shear of the differential equation for transverse vibrations of prismatic bar”, Philosophical Magazine Series, 6:245 (1921), 744–746  crossref


© Steklov Math. Inst. of RAS, 2026