Love wave in a classical linear elastic half-space covered by a surface layer described by the couple stress theory. (English) Zbl 1430.74065
Summary: A Love wave is derived for a new physical configuration in which a surface layer described by the couple stress theory covers a classical elasticity half-space. The dispersion equation is derived analytically when the thickness of the surface layer approaches zero. The correctness of the dispersion equation is confirmed via the second derivation path, namely the surface elasticity. The membrane with microstructure is described by the surface elasticity which significantly simplifies the derivation. New propagation features deduced from the dispersion curves are discussed.
References:
| [1] | Mindlin, R.D., Tiersten, H.F.: Effects of couple-stress in linear elasticity. Arch. Ration. Mech. Anal. 11, 415-488 (1962) · Zbl 0112.38906 · doi:10.1007/BF00253946 |
| [2] | Toupin, R.A.: Elastic materials with couple stresses. Arch. Ration. Mech. Anal. 11, 385-414 (1962) · Zbl 0112.16805 · doi:10.1007/BF00253945 |
| [3] | Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51-78 (1964) · Zbl 0119.40302 · doi:10.1007/BF00248490 |
| [4] | Mindlin, R.D., Eshel, N.N.: On first strain gradient theories in linear elasticity. Int. J. Solids Struct. 4, 109-124 (1968) · Zbl 0166.20601 · doi:10.1016/0020-7683(68)90036-X |
| [5] | Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477-508 (2003) · Zbl 1077.74517 · doi:10.1016/S0022-5096(03)00053-X |
| [6] | Askes, H., Aifantis, E.C.: Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results. Int. J. Solids Struct. 48, 1962-1990 (2011) · doi:10.1016/j.ijsolstr.2011.03.006 |
| [7] | Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731-2743 (2002) · Zbl 1037.74006 · doi:10.1016/S0020-7683(02)00152-X |
| [8] | Hadjesfandiari, A.R., Dargush, G.F.: Couple stress theory for solids. Int. J. Solids Struct. 48, 2496-2510 (2011) · doi:10.1016/j.ijsolstr.2011.05.002 |
| [9] | Neff, P., Münch, I., Ghiba, I.D., Madeoe, A.: On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush. Int. J. Solids Struct. 81, 233-243 (2016) · doi:10.1016/j.ijsolstr.2015.11.028 |
| [10] | Achenbach, A.D.: Wave Propagation in Elastic Solids. North-Holland, Amsterdam (1973) · Zbl 0268.73005 |
| [11] | Vardoulakis, I., Georgiadis, H.G.: SH surface waves in a homogeneous gradient-elastic half-space with surface energy. J. Elast. 47, 147-165 (1997) · Zbl 0912.73016 · doi:10.1023/A:1007433510623 |
| [12] | Gourgiotis, P.A., Georgiadis, H.G.: Torsional and SH surface waves in an isotropic and homogenous elastic half-space characterized by the Toupin-Mindlin gradient theory. Int. J. Solids Struct. 62, 217-228 (2015) · doi:10.1016/j.ijsolstr.2015.02.032 |
| [13] | Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291-323 (1975) · Zbl 0326.73001 · doi:10.1007/BF00261375 |
| [14] | Murdoch, A.I.: The propagation of source waves in bodies with material boundaries. J. Mech. Phys. Solids 24, 137-146 (1976) · Zbl 0342.73017 · doi:10.1016/0022-5096(76)90023-5 |
| [15] | Fan, H., Xu, L.M.: Decay rates in nano tubes with consideration of surface elasticity. Mech. Res. Commun. 73, 113-116 (2016) · doi:10.1016/j.mechrescom.2016.02.013 |
| [16] | Wang, X., Fan, H.: A piezoelectric screw dislocation in a bimaterial with surface piezoelectricity. Acta Mech. 226, 3317-3331 (2015) · Zbl 1329.74089 · doi:10.1007/s00707-015-1382-7 |
| [17] | Xu, L.M., Wang, X., Fan, H.: Anti-plane waves near an interface between two piezoelectric half-spaces. Mech. Res. Commun. 67, 8-12 (2015) · doi:10.1016/j.mechrescom.2015.04.006 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
