Dynamic Response of Tunnel Structures in Inhomogeneous Medium Under SH Wave: Shear Modulus in Quadratic Functional Form
Source abstract
Abstract
The task of this work is to study the scattering of SH waves by homogeneous tunnel structures in an unbounded inhomogeneous medium. The shear modulus is assumed to be a function of coordinates (x,y). A two-dimensional scattering model is established. Selecting different inhomogeneous parameters, the medium has different properties, expressed as a rigid variation. The stress concentration phenomenon of the structure is analyzed for material design. Based on the complex function theory, the expressions of wave field in the tunnel are derived. The stress concentration phenomenon on the tunnel is discussed with numerical examples. The distribution of dynamic stress concentration factor on the inner and outer boundaries is analyzed under different influencing factors. Finally, it is found that the distribution of dynamic stress concentration factor is significantly affected by the inhomogeneous parameters and reference wave numbers of the medium.
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Research context
OpenAlex topics: Geotechnical Engineering and Underground Structures · Seismic Waves and Analysis · Rock Mechanics and Modeling
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References (26)
Show source-provided references
1. Pao YH, Mao CC. Diffraction of elastic waves and dynamic stress concentration. New York: Crane and Russak; 1973.10.1115/1.3423178 ↗
2. Popov A, Kovalchuk V. Parametric representation of wave propagation in nonuniform media (both in transmission and stop bands). Math Meth Appl Sci. 2013;36(11):1350–62.10.1002/mma.2687 ↗
3. Urena M, Benito JJ, Urena F, Salete E, Gavete L. Application of generalised finite differences method to reflection and transmission problems in seismic SH waves propagation. Math Meth Appl Sci. 2017;41(6):2328–39.10.1002/mma.4268 ↗
4. Sing H, Das A, Mistri KC, Chattopadhyay A. Green’s function approach to study the propagation of SH-wave in piezoelectric layer influenced by a point source. Math Meth Appl Sci. 2017;40(13):4771–84.
5. Han X, Liu GR. Effects of SH waves in a functionally graded plate. Mech Res Commun. 2002;29(5):327–38.10.1016/S0093-6413(02)00316-6 ↗
6. Martin PA. Scattering by a cavity in an exponentially graded half-space. J Appl Mech Trans ASME. 2009;76(3):540–5.10.1115/1.3086585 ↗
7. Liu QJ, Zhao MJ, Zhang C. Antiplane scattering of SH waves by a circular cavity in an exponentially graded half space. Int J Eng Sci. 2014;78:61–72.10.1016/j.ijengsci.2014.02.006 ↗
8. Ghafarollahi A, Shodja HM. Scattering of SH-waves by an elliptic cavity/crack beneath the interface between functionally graded and homogeneous half-spaces via multipole expansion method. J Sound Vib. 2018;435:372–89.10.1016/j.jsv.2018.08.022 ↗
9. Zhang LL, Fang XQ, Liu JX. The multiple scattering of non-homogeneous shear waves from two cavities in functionally graded materials. Philos Mag. 2010;90(24):3375–87.10.1080/14786435.2010.485584 ↗
10. Golub MV, Fomenko SI, Bui TQ. Transmission and band gaps of elastic SH waves in functionally graded periodic laminates. Int J Solids Struct. 2012;49(2):344–54.10.1016/j.ijsolstr.2011.10.013 ↗
11. Hei BP, Yang ZL, Sun BT, Wang Y. Modelling and analysis of the dynamic behavior of inhomogeneous continuum containing a circular inclusion. Appl Math Model. 2015;39(23–24):7364–74.10.1016/j.apm.2015.03.015 ↗
12. Hei BP, Yang ZL, Sun BT, Liu DK. Dynamic stress analysis around a circular cavity in two-dimensional inhomogeneous medium with density variation. J Mech. 2016;32(5):519–26.10.1017/jmech.2016.7 ↗
13. Kundu S, Manna S, Gupta S. Propagation of SH-wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi-infinite media. Math Method Appl Sci. 2015;38(9):1926–36.10.1002/mma.3203 ↗
14. Jiang GXX, Yang ZL, Sun C, Sun BT, Yang Y. Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves. Math Meth Appl Sci. 2020;43(11):6888–902.10.1002/mma.6431 ↗
15. Bednarik M, Cervenka M, Lotton P, Simon L. Analytical solutions for elastic SH-waves propagating through an isotropic inhomogeneous layer. Compos Struct. 2019;220:875–87.10.1016/j.compstruct.2019.04.053 ↗
16. Daros CH. Green’s function for SH-waves in inhomogeneous anisotropic elastic solid with power-function velocity variation. Wave Motion. 2013;50(2):101–10.10.1016/j.wavemoti.2012.07.004 ↗
17. Singh BM, Rokne J. Propagation of SH waves in layered functionally gradient piezoelectric–piezomagnetic structures. Philos Mag. 2013;93(14):1690–700.10.1080/14786435.2012.753483 ↗
18. Negi A, Singh AK, Yadav RP. Analysis on dynamic interfacial crack impacted by SH-wave in bi-material poroelastic strip. Compos Struct. 2020;233: 111639.10.1016/j.compstruct.2019.111639 ↗
19. Manolis GD, Dineva PS, Rangelov TV. Dynamic fracture analysis of a smoothly inhomogeneous plane containing defects by BEM. Eng Ana Bound Elem. 2012;36(5):727–37.10.1016/j.enganabound.2011.11.010 ↗
20. Gamer U. Dynamic stress concentration in an elastic half space with a semi-circular cavity excited by SH waves. Int J Solids Struct. 1977;13(7):675–81.10.1016/0020-7683(77)90049-X ↗
21. Tao M, Zhao R, Du K. Dynamic stress concentration and failure characteristics around elliptical cavity subjected to impact loading. Int J Solids Struct. 2020;191:401–17.10.1016/j.ijsolstr.2020.01.009 ↗
22. Meade KP, Keer LM. Dynamic response of an embedded rectangular foundation to antiplane shear waves. Int J Solids Struct. 1982;18(3):249–61.10.1016/0020-7683(82)90007-5 ↗
23. Kara HF, Aydogdu M. Dynamic response of a functionally graded tube embedded in an elastic medium due to SH-Waves. Compos Struct. 2018;206:22–32.10.1016/j.compstruct.2018.08.032 ↗
24. Jang P, Paek U, Jong K, Yun D, Kim C, Ri S. Dynamic analysis of SH wave by a three-layer inclusion near interface in bi-material half space. AIP Adv. 2020;10(5): 055107.10.1063/1.5143595 ↗
25. Sheikhhassani R, Dravinski M. Dynamic stress concentration for multiple multilayered inclusions embedded in an elastic half-space subjected to SH-waves. Wave Motion. 2016;62:20–40.10.1016/j.wavemoti.2015.11.002 ↗
26. Liu DK, Gai BZ, Tao GY. Applications of the method of complex functions to dynamic stress concentrations. Wave Motion. 1982;4(3):293–304.10.1016/0165-2125(82)90025-7 ↗