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Acta Mechanica
Published in: Acta Mechanica 9/2021

24-06-2021 | Original Paper

Rayleigh-type surface wave in nonlocal isotropic diffusive materials

Authors: Baljinder Kaur, Baljeet Singh

Published in: Acta Mechanica | Issue 9/2021

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Abstract

In this paper, the nonlocal non-Fick diffusion elasticity theory is applied to study the propagation of Rayleigh-type surface waves along the stress-free surface of an isotropic diffusive elastic half-space. The equations governing the motion in an isotropic nonlocal non-Fick diffusion elastic medium are specialized for a plane. The appropriate surface wave solutions of the resulting two-dimensional governing equations are obtained which satisfy the required decay condition in the half-space. Then, the relevant boundary conditions prescribed at the free surface are used to derive a characteristic equation of Rayleigh-type surface wave. In the absence of nonlocality and mass diffusion parameters, the classical Rayleigh wave equation is obtained as a particular case. A numerical example is setup to illustrate the effects of nonlocality and mass diffusion parameters on the speed of the Rayleigh wave.
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Literature
1.
Eringen, A.C.: Nonlocal Continuum Field Theories. Springer Verlag, New York (2001)MATH
2.
Voyiadjis, G.Z.: Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer Nature, Berlin (2019)CrossRef
3.
Eringen, A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–435 (1972)CrossRef
4.
Narasimhan, M.N.L., McCay, B.M.: Dispersion of surface waves in nonlocal dielectric fluids. Arch. Mech. 33, 385–400 (1981)MATH
5.
Inan, E., Eringen, A.C.: Nonlocal theory of wave propagation in thermoelastic plates. Int. J. Eng. Sci. 29, 831–843 (1991)CrossRef
6.
Ke, L.-L., Wang, Y.-S., Wang, Z.-D.: Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory. Compos. Struct. 94, 2038–2047 (2012)CrossRef
7.
Sapora, A., Cornetti, P., Carpinteri, A.: Wave propagation in nonlocal elastic continua modelled by a fractional calculus approach. Commun. Nonlinear Sci. Numer. Simul. 18, 64–73 (2013)MathSciNetCrossRef
8.
Roy, I., Acharya, D.P., Acharya, S.: Rayleigh wave in a rotating nonlocal magnetoelastic half-plane. J. Theor. Appl. Mech. Sofia 45, 61–78 (2015)MathSciNetCrossRef
9.
Tong, L., Yu, Y., Hu, W., Shi, W., Xu, C.: On wave propagation characteristics in fluid saturated porous materials by a nonlocal Biot theory. J. Sound Vib. 379, 106–118 (2016)CrossRef
10.
Singh, D., Kaur, G., Tomar, S.K.: Waves in nonlocal elastic solid with voids. J. Elast. 128, 84–114 (2017)MathSciNetMATH
11.
Kaur, G., Singh, D., Tomar, S.K.: Rayleigh-type wave in a nonlocal elastic solid with voids. Eur. J. Mech. A-Solid 71, 134–150 (2018)MathSciNetCrossRef
12.
Tung, D.X.: Dispersion equation of Rayleigh waves in transversely isotopic nonlocal piezoelastic solid half-space. Vietnam J. Mech. 41, 363–371 (2019)CrossRef
13.
Ma, Y.-S., Ke, L.-L., Wang, Y.-Z., Wang, Y.-S.: Wave propagation analysis of piezoelectric nanoplates based on the nonlocal theory. Int. J. Struct. Stab. Dyn. 18, 1850060 (2018)MathSciNetCrossRef
14.
Yan, D.-J., Chen, A.-L., Wang, Y.-S., Zhang, C., Golub, M.: Propagation of guided elastic waves in nanoscale layered periodic piezoelectric composites. Eur. J. Mech. A-Solid 66, 158–167 (2017)MathSciNetCrossRef
15.
16.
Li, C., Guo, H., Tian, X., He, T.: Nonlocal diffusion-elasticity based on nonlocal mass transfer and nonlocal elasticity and its application in shock-induced responses analysis. Mech. Adv. Mater. Struct. 12, 1–12 (2019)
17.
Li, C., He, T., Tian, X.: Nonlocal theory of thermoelastic diffusive materials and its application in structural dynamic thermo-elasto-diffusive responses analysis. Waves Random Complex Media 21, 1–30 (2020)
18.
Li, C., Guo, H., Tian, X.: A size-dependent generalized thermoelastic diffusion theory and its application. J. Therm. Stresses 40, 603–626 (2017)CrossRef
19.
Li, C., He, T., Tian, X.: Transient responses of nanosandwich structure based on size-dependent generalized thermoelastic diffusion theory. J. Therm. Stresses 42, 1171–1191 (2019)CrossRef
20.
Yu, Y.J., Tian, X.G., Xiong, Q.L.: Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity. Eur. J. Mech. A/Solids 60, 238–253 (2016)MathSciNetCrossRef
21.
Hosseini, S.A., Abolbashari, M.H., Hosseini, S.M.: Shock-induced molar concentration wave propagation and coupled non-Fick diffusion-elasticity analysis using an analytical method. Acta Mechanica 225, 3591–3599 (2014)MathSciNetCrossRef
22.
Sobolev, S.L.: Nonlocal diffusion models: Application to rapid solidification of binary mixtures. Int. J. Heat Mass Transf. 71, 295–302 (2014)CrossRef
23.
Yu, Y.J., Tian, X.G., Liu, X.R.: Size-dependent generalized thermoelasticity using Eringen’s nonlocal model. Eur. J. Mech. A/Solids 51, 96–106 (2015)MathSciNetCrossRef
24.
Zhang, L.L., Liu, J.X., Fang, X.Q., Nie, G.Q.: Surface effect on size-dependent wave propagation in nanoplates via nonlocal elasticity. Philos. Mag. 94, 2009–2020 (2014)CrossRef
25.
Ebrahimi, F., Barati, M.R.: Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams. Waves Random Complex Media 28, 326–342 (2018)CrossRef
26.
Lim, C.W., Zhang, G., Reddy, J.N.: A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 78, 298–313 (2015)MathSciNetCrossRef
27.
Asemi, H.R., Asemi, S.R., Farajpour, A., Mohammadi, M.: Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads. Phys. E Low Dimens. Syst. Nanostruct. 68, 112–122 (2015)CrossRef
28.
29.
30.
Sobolev, S.L.: Discrete space-time model for heat conduction: Application to size-dependent thermal conductivity in nano-films. Int. J. Heat Mass Transf. 108, 933–939 (2017)CrossRef
31.
Lu, P., Lee, H.P., Lu, C., Zhang, P.Q.: Dynamic properties of flexural beams using a nonlocal elasticity model. J. Appl. Phys. 99, 073510 (2006)CrossRef
32.
Miandoab, E.M., Pishkenari, H.N., Yousefi-Koma, A., Hoorzad, H.: Polysilicon nano-beam model based on modified couple stress and Eringen’s nonlocal elasticity theories. Phys. E Low Dimens. Syst. Nanostruct. 63, 223–228 (2014)CrossRef
33.
Martowicz, A., Bryła, J., Staszewski, W.J., Ruzzene, M., Uhl, T.: Nonlocal elasticity in shape memory alloys modeled using peridynamics for solving dynamic problems. Nonlinear Dyn. 97, 1911–1935 (2019)CrossRef
34.
Ilcewicz, L., Narasimhan, M., Wilson, J.: An experimental verification of nonlocal fracture criterion. Eng. Fract. Mech. 14, 801–808 (1981)CrossRef
35.
Lim, C.W.: On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection. Appl. Math. Mech. 31, 37–54 (2010)MathSciNetCrossRef
36.
Farajpour, A., Rastgoo, A., Farajpour, M.R.: Nonlinear buckling analysis of magneto-electro-elastic CNT-MT hybrid nanoshells based on the nonlocal continuum mechanics. Compos. Struct. 180, 179–191 (2017)CrossRef
37.
Li, C., Lai, S.K., Yang, X.: On the nano-structural dependence of nonlocal dynamics and its relationship to the upper limit of nonlocal scale parameter. Appl. Math. Model. 69, 127–141 (2019)MathSciNetCrossRef
38.
Lu, P.: Dynamic analysis of axially prestressed micro/nanobeam structures based on nonlocal beam theory. J. Appl. Phys. 101, 073504 (2007)CrossRef
39.
Rayleigh, L.: On waves propagated along the plane surface of an elastic solid. Proc. R. Soc. Lond. Ser. A 17, 4–11 (1885)MathSciNetMATH
Metadata
Title
Rayleigh-type surface wave in nonlocal isotropic diffusive materials
Authors
Baljinder Kaur
Baljeet Singh
Publication date
24-06-2021
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 9/2021
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-021-03016-2

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