By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures.
CallisterWDRethwischDG. Materials science and engineering: an introduction. 9th ed.Hoboken, NJ: John Wiley & Sons, 2014.
2.
ZhaoYPWangLSYuTX. Mechanics of adhesion in MEMS—a review. J Adhes Sci Technol2003; 17(4): 519–546.
3.
RoseJL. Ultrasonic waves in solid media. Cambridge: Cambridge University Press, 2004.
4.
MindlinRDTierstenHF. Effects of couple-stresses in linear elasticity. Arch Ration Mech An1962; 11(1): 415–448.
5.
MindlinRD. Micro-structure in linear elasticity. Arch Ration Mech An1964; 16(1): 51–78.
6.
EringenAC. Linear theory of micropolar elasticity. J Math Mech1966; 15(6): 909–923.
7.
EringenAC. Nonlocal continuum field theories. New York: Springer, 2002.
8.
GraffKFPaoYH. The effects of couple-stresses on the propagation and reflection of plane waves in an elastic half-space. J Sound Vib1967; 6(2): 217–229.
9.
ParfittVREringenAC. Reflection of plane waves from the flat boundary of a micropolar elastic half-space. J Acoust Soc Am1969; 45(5): 1258–1272.
10.
GourgiotisPAGeorgiadisHGNeocleousI. On the reflection of waves in half-spaces of microstructured materials governed by dipolar gradient elasticity. Wave Motion2013; 50(3): 437–455.
11.
VardoulakisIGeorgiadisHG. SH surface waves in a homogeneous gradient-elastic half-space with surface energy. J Elasticity1997; 47(2): 147–165.
12.
GeorgiadisHGVardoulakisILykotrafitisG. Torsional surface waves in a gradient-elastic half-space. Wave Motion2000; 31(4): 333–348.
13.
GourgiotisPAGeorgiadisHG. Torsional and SH surface waves in an isotropic and homogenous elastic half-space characterized by the Toupin–Mindlin gradient theory. Int J Solids Struct2015; 62: 217–228.
14.
AchenbachJD. Wave propagation in elastic solids. Amsterdam: North-Holland, 1973.
15.
RayleighL. On waves propagated along the plane surface of an elastic solid. P Lond Math Soc1885; s1–s17(1): 4–11.
16.
EringenAC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys1983; 54(9): 4703–4710.
17.
GeorgiadisHGVelgakiEG. High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects. Int J Solids Struct2003; 40(10): 2501–2520.
18.
GeorgiadisHGVardoulakisIVelgakiEG. Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity. J Elasticity2004; 74(1): 17–45.
19.
ChiriţăSGhibaID. Rayleigh waves in Cosserat elastic materials. Int J Eng Sci2012; 51: 117–127.
20.
VavvaMGProtopappasVCGergidisLN, et al. Velocity dispersion of guided waves propagating in a free gradient elastic plate: application to cortical bone. J Acoust Soc Am2009; 125(5): 3414–3427.
21.
GhodratiBYaghootianAGhanbar ZadehA, et al. Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories. Wave Random Complex2018; 28(1): 15–34.
22.
EremeyevVARosiGNailiS. Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses. Math Mech Solids2019; 24(8): 2526–2535.
23.
SolyaevYLurieS. Electric field, strain and inertia gradient effects on anti-plane wave propagation in piezoelectric materials. J Sound Vib2021; 494: 115898.
24.
YangWJDengQLiangX, et al. Lamb wave propagation with flexoelectricity and strain gradient elasticity considered. Smart Mater Struct2018; 27(8): 085003.
25.
YangWJLiangXDengQ, et al. Rayleigh wave propagation in a homogeneous centrosymmetric flexoelectric half-space. Ultrasonics2020; 103: 106105.
26.
LoveAEH. Some problems of geodynamics. Cambridge: Cambridge University Press, 1911.
27.
TolstoyIUsdinE. Dispersive properties of stratified elastic and liquid media: a ray theory. Geophysics1953; 18(4): 844–870.
28.
EwingWMJardetzkyWSPressF. Elastic waves in layered media. New York: McGraw Hill, 1957.
29.
FanHXuLM. Love wave in a classical linear elastic half-space covered by a surface layer described by the couple stress theory. Acta Mech2018; 229(12): 5121–5132.
30.
FanHLongJM. In-plane surface wave in a classical elastic half-space covered by a surface layer with microstructure. Acta Mech2020; 231(11): 4463–4477.
31.
MidyaGK. On Love-type surface waves in homogeneous micropolar elastic media. Int J Eng Sci2004; 42(11–12): 1275–1288.
32.
LongJMFanH. SH surface wave propagating in a strain-gradient layered half-space. Acta Mech2021; 232(3): 1061–1074.
33.
SuikerASJChangCSDe BorstR, et al. Surface waves in a stratified half space with enhanced continuum properties. Part 2: analysis of the wave characteristics in regard to high-speed railway tracks. Eur J Mech A: Solid1999; 18(5): 769–784.
