Abstract
The objective of the paper is to investigate the propagation behavior of horizontally polarized shear waves (SH-waves) in an inhomogeneous fiber-reinforced layer which is sandwiched between two microstructural half-spaces. The half-spaces are modeled using size-dependent consistent couple stress theory. The mathematical formulations of consistent couple stress theory contains a length scale parameter called characteristic length. Characteristic length is comparable with the size of internal microstructure of the material and introduces the role of size dependency into the problem. The propagation behavior of SH-waves is investigated in an inhomogeneous fiber-reinforced layer under two different scenarios, first when the layer is perfectly attached to the half-spaces and second when the layer is in imperfect contact with the half-spaces. Dispersion and damping relations are calculated for the propagation of SH-waves in both cases separately using suitable boundary conditions. Some special cases are also generated under different conditions. The impact of various parameters such as characteristic length, inhomogeneity, reinforcement, and imperfectness are manifested graphically on the phase and damping velocities of the SH-waves.
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References
Abbas IA, Abd-alla AN (2011) Generalised magneto-thermoelasticity in a fiber-reinforced anisotropic half-space. Int J Thermophys 32(5):1071–1085. https://doi.org/10.1007/s10765-011-0957-3
Belfield AJ, Rogers TG, Spencer AJM (1983) Stress in elastic plates reinforced by fibres lying in concentric circles. J Mech Phys Solids 31(1):25–54. https://doi.org/10.1016/0022-5096(83)90018-2
Chen WQ, Cai JB, Ye GR, Wang YF (2004) Exact three-dimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring interlaminar bonding imperfections modeled by a general spring layer. Int J Solids Struc 41(18–19):5247–5263. https://doi.org/10.1016/j.ijsolstr.2004.03.010
Cosserat E, Cosserat F (1909) Théorie des corps déformables (Theory of deformable bodies) A. Hermann et Fils, Paris
Deep S, Sharma V (2022) Love wave propagation in viscoelastic layer sandwiched between fiber-reinforced layer and consistent couple stress substrate. Iran J Sci Technol: Trans Mech Eng 46:225–235. https://doi.org/10.1007/s40997-020-00411-3
Deep S, Goyal R, Sharma V (2022) Dispersion of Rayleigh waves in an elastic layer imperfectly attached to a microcontinuum substrate. Mech Solids 57(4):870–882. https://doi.org/10.3103/S0025654422040069
Di Michele F, Styahar A, Pera D, May J, Aloisio R, Rubino B, Marcati P (2022) Fault shape effect on SH waves using finite element method. J Seismol 26:417–437. https://doi.org/10.1007/s10950-022-10075-y
Dravinski M, Yu MC (2011) Scattering of plane harmonic SH waves by multiple inclusions. Geophys J Int 186(3):1331–1346. https://doi.org/10.1111/j.1365-246X.2011.05111.x
Eringen AC (1966) Linear theory of micropolar elasticity. J Math Mech 15:909–924
Fan H, Xu L (2018) Love wave in a classical linear elastic half-space covered by a surface layer described by the couple stress theory. Acta Mech 229:5121–5132. https://doi.org/10.1007/s00707-018-2293-1
Ferreira FV, Pinheiro IF, De Souza SF, Mei LHI, Lona LMF (2019) Polymer composites reinforced with natural fibers and nanocellulose in the automotive industry: a short review. J Compos Sci 3(2):51. https://doi.org/10.3390/jcs3020051
Georgiadis HG, Vardoulakis I, Velgaki E (2004) Dispersive rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity. J Elast 74(1):17–45. https://doi.org/10.1023/B:ELAS.0000026094.95688.c5
Goyal R, Kumar S (2019) Dispersion of love waves in size-dependent substrate containing finite piezoelectric and viscoelastic layers. Int J Mech Mater Des 15:767–790. https://doi.org/10.1007/s10999-019-09441-5
Goyal R, Kumar S, Sharma V (2020) A size-dependent micropolar-piezoelectric layered structure for the analysis of love wave. Waves Rand Compl Media 30(3):544–561. https://doi.org/10.1080/17455030.2018.1542186
Hadjesfandiari AR, Dargush GF (2011) Couple stress theory for solids. Int J Solids Struct 48(18):2496–2510. https://doi.org/10.1016/j.ijsolstr.2011.05.002
Ilyashenko AV, Kuznetsov SV (2017) Theoretical aspects of applying love and SH-waves to nondestructive testing of stratified media. Russ J Nondestruct Test 53(9):597–603. https://doi.org/10.1134/S1061830917090078
Josse F, Bender F, Cernosek RW (2001) Guided shear horizontal surface acoustic wave sensors for chemical and biochemical detection in liquids. Anal Chem 73(24):5937–5944. https://doi.org/10.1021/ac010859e
Kaur T, Sharma SK, Singh AK (2017) Shear wave propagation in vertically heterogeneous viscoelastic layer over a micropolar elastic half-space. Mech Adv Mater Struct 24(2):149–156. https://doi.org/10.1080/15376494.2015.1124948
Kocaturk T, Akbas SD (2013) Wave propagation in a microbeam based on the modified couple stress theory. Struct Eng Mech 46(3):417–431. https://doi.org/10.12989/sem.2013.46.3.417
Koiter WT (1964) Couple stresses in the theory of elasticity, I and II. Proc Ned Akad Wet B 67:17–44
Kuznetsov SV (2006) SH-waves in laminated plates. Q Appl Math 64(1):153–165. https://doi.org/10.1090/S0033-569X-06-00992-1
Kuznetsov SV (2021) Extinction of Stoneley waves in stratified media with diffused interfaces. Int J Mech Mater Des 17:601–607. https://doi.org/10.1007/s10999-021-09549-7
Lee S, Kim KB, Kim YI (2011) Love wave SAW biosensors for detection of antigen-antibody binding and comparison with SPR biosensor. Food Sci Biotechnol 20(5):1413–1418. https://doi.org/10.1007/s10068-011-0194-3
Li P, Jin F (2012) Bleustein-Gulyaev waves in a transversely isotropic piezoelectric layered structure with an imperfectly bonded interface. Smart Mater Struct 21(4):045009. https://doi.org/10.1088/0964-1726/21/4/045009
Liu Q, Zhao M, Zhang C (2014) Antiplane scattering of SH waves by a circular cavity in an exponentially graded half space. Int J Eng Sci 78:61–72. https://doi.org/10.1016/j.ijengsci.2014.02.006
Miao H, Li F (2021) Shear horizontal wave transducers for structural health monitoring and nondestructive testing: a review. Ultrasonics 114:106355. https://doi.org/10.1016/j.ultras.2021.106355
Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Ration Mech Anal 11:415–448
Nakamura K (2007) Shear-horizontal piezoelectric surface acoustic waves. Jpn J Appl Phys 46(7):4421. https://doi.org/10.1143/JJAP.46.4421
Pang Y, Feng W, Liu J, Zhang C (2019) SH wave propagation in a piezoelectric/piezomagnetic plate with an imperfect magnetoelectroelastic interface. Waves Random Compl Media 29(3):580–594. https://doi.org/10.1080/17455030.2018.1539277
Qingzeng MA, Jingpin J, Ping HU, Xi Z, Bin WU, Cunfu HE (2014) Excitation and detection of shear horizontal waves with electromagnetic acoustic transducers for nondestructive testing of plates. Chin J Mech Eng 27(2):428–436. https://doi.org/10.3901/CJME.2014.02.428
Rostocki AJ, Siegoczyński RM, Kiełczyński P, Szalewski M (2010) An application of Love SH waves for the viscosity measurement of triglycerides at high pressures. High Press Res 30(1):88–92. https://doi.org/10.1080/08957951003622289
Sahu SA, Saroj PK, Paswan B (2014) Shear waves in a heterogeneous fiber-reinforced layer over a half-space under gravity. Int J Geomech 15(2):04014048. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000404
Said SM, Othman MIA (2016) Gravitational effect on a fiber-reinforced thermoelastic medium with temperature-dependent properties for two different theories. Iran J Sci Technol Trans Mech Eng 40:223–232. https://doi.org/10.1007/s40997-016-0014-8
Sharma V, Kumar S (2016) Influence of microstructure, heterogeneity and internal friction on SH waves propagation in a viscoelastic layer overlying a couple stress substrate. Struct Eng Mech 57(4):703–716. https://doi.org/10.12989/sem.2016.57.4.703
Sharma V, Kumar S (2018) Dispersion of Rayleigh waves in a microstructural couple stress substrate loaded with liquid layer under the effects of gravity. Arch Acoust 43(1):11–20. https://doi.org/10.24425/118076
Sharma V, Sharma V (2020) Love waves in fiber-reinforced layer imperfectly bonded to microstructural couple stress substrate. J Theor Appl Mech 58(1):221–232. https://doi.org/10.15632/jtam-pl/115476
Sharma V, Goyal R, Kumar S (2020) Love waves in a layer with void pores over a microstructural couple stress substrate with corrugated boundary surfaces. J Braz Soc Mech Sci 42(4):1–16. https://doi.org/10.1007/s40430-020-2262-1
Simonetti F, Cawley P (2004) On the nature of shear horizontal wave propagation in elastic plates coated with viscoelastic materials. Proc Math Phys Eng Sci 460(2048):2197–2221. https://doi.org/10.1098/rspa.2004.1284
Vardoulakis I, Georgiadis HG (1997) SH surface waves in a homogeneous gradient-elastic half-space with surface energy. J Elast 47:147–165. https://doi.org/10.1023/A:1007433510623
Voigt W (1887) Theoretische Studien über die Elasticitätsverhältnisse der Krystalle (Theoretical studies in the elastic behavior of crystals). Abh. Gesch Wissenschaften, p 34
Zagho MM, Hussein EA, Elzatahry AA (2018) Recent overviews in functional polymer composites for biomedical applications. Polymers 10(7):739. https://doi.org/10.3390/polym10070739
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Deep, S., Sharma, V. Effects of Microstructures, Heterogeneity, and Imperfectness on Propagation of SH-Waves in a Fiber-Reinforced Layer Sandwiched Between Two Microstructural Half-Spaces. Iran J Sci Technol Trans Mech Eng 47, 1161–1176 (2023). https://doi.org/10.1007/s40997-022-00570-5
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DOI: https://doi.org/10.1007/s40997-022-00570-5