In this paper, the scattering of SH wave by a nano elliptical hole embedded the infinite inhomogeneous medium is studied. First, the displacement governing equation with variable coefficients is transformed into the complex Helmholtz equation by using complex variable function and conformal transformation. By the wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young–Laplace equation, we obtain the boundary conditions at nano elliptical hole; then the field equations satisfied by the boundary conditions are attributed to solving a set of infinite algebraic equations. The numerical results show that when the size of the elliptical hole reaches the nanometer level, the influences of surface energy, inhomogeneous coefficients, and wave number on the dynamic stress concentration factor near the hole are significant.
PaoYHMowCCAchenbachJD. Diffraction of elastic waves and dynamic stress concentrations. J Appl Mech1973; 40: 213–219.
2.
LinHLiuDK. Scattering of SH wave around a circular cavity in half space. Earthq Eng Vibrat2002; 22(2): 9–16.
3.
ChenZG. Dynamic stress concentration near arbitrarily shaped holes at interfaces under the action of SH waves. J Solid Mech2006; 27(4): 408–414.
4.
ChenZGLiuDK. Dynamic response on a shallowly cavity of arbitray shape impacted by vertical SH-wave. Earthq Eng Eng Vib2004; 24: 32–36.
5.
ShiWP. Scattering of SH waves by elliptical holes in quarter space. Mech Strength2010; 32(5): 774–780.
6.
YangZLLiuDKSunBT, et al. Scattering of SH waves and dynamic stress concentration by half-space movable rigid cylinders. Eng Mech2009; 26(4): 51–56.
7.
LiuDKLiuHW. SH wave scattering and dynamic stress concentration near an interfacial circular hole. J Mech1998; 30(5): 597–604.
8.
LiuDKGuangGQ. Scattering of SH waves by a semicircular projection near a shallow buried circular hole. J Mech2006; 38(2): 209–218.
9.
GosarP. Multiple small angle scattering of waves by an inhomogeneous medium. IL Nuovo Cimento1956; 4(4): 688–702.
10.
GosarP. A new method for solving multiple scattering problems in inhomogeneous media. IL Nuovo Cimento1957; 5(6): 1437–1455.
11.
MaulikTN. Propagation of surface waves in heterogeneous media containing a low velocity channel. Pure Appl Geophys1965; 60(1): 42–50.
12.
JiangGXX. Dynamic stress concentration in the entrained perimeter of different inhomogeneous media under the action of SH waves. Harbin, China: Harbin Engineering University, 2020.
13.
DingXHQiHZhaoYB. Scattering of SH waves by elliptical entrainment in a right-angle domain and ground shaking. Eng Mech2016; 33(7): 48–54, 83.
14.
GurtinMEMurdochAI. Surface stress in solids. Int J Solids Struct1978; 14(6): 431–440.
15.
DingrevilleRQuJCherkaouiM. Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids2005; 53(8): 1827–1854.
16.
WangGFWangTJFengXQ. Surface effects on the diffraction of plane compressional waves by a nanosized circular Hole. Appl Phys Lett2006; 89: 1–3.
17.
OuZYWangGFWangTJ. Elastic fields around a nanosized spheroidal cavity under arbitrary uniform remote loadings. Eur J Mech A Solids2009; 28(1): 110–120.
18.
ZhangQFWangGFSchiavoneP. Diffraction of plane compressional waves by an array of nanosized cylindrical holes. J Appl Mech2011; 78(2): 856–875.
19.
WuHMOuZY. Complex-variable function solution for SH-wave scattering from nanocircular holes. J Appl Mech2021; 38(02): 763–769.
20.
RuYWangGFWangTJ. Diffractions of elastic waves and stress concentration near a cylindrical nano-inclusion incorporating surface effect. J Vib Acoust2009; 131: 061011.
21.
OuZYSunYQ. Surface effects on the scatter of SH-wave by a shallow buried the elliptical Hole. Open J Appl Sci2019; 9: 480–491.
22.
ZhangDLiuYWShangKR. Mechanism of mismatch dislocation nucleation at thin film interfaces with nanoscale circular pore surfaces. Eng Mech2013; 30(10): 282–287, 295.
23.
XieJLiHLiFJ, et al. Multilayer heterostructure inhomogeneous model for the functionally graded spherical shell with rotation effect for arbitrarily varying material properties. Compos Struct2024; 339: 118145.
24.
ChenTChiuMSWengCN. Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. J Appl Phys2006; 100(7): 074308.
25.
HeiBPYangZLWangY, et al. Dynamic analysis of elastic waves by an arbitrary cavity in an inhomogeneous medium with density variation. Math Mech Solids2016; 21(8): 931–940.
26.
JiangGXXYangZL. Analytical study of SH wave scattering by a cylindrical cavity in the two-dimensional and approximately linear inhomogeneous medium. Waves Random Complex2020; 31: 1799–1817.
27.
HeLHLiZR. Impact of surface stress on stress concentration. Int J Solids Struct2006; 43(20): 6208–6219.
