Abstract
The complex function method is applied in the solution of the scattering problem for an irregularly shaped boundary in an infinite inhomogeneous elastic medium, which is deduced from the scattering problem in a homogeneous one. The potential function of the scattering wave which is generated by the irregularly boundary is obtained by applying the complex function method in the inhomogeneous medium. The reduced Helmholtz equation with variable coefficients is solved by separation of variables. Then, the potential function is expressed as the complex domain functions series. By truncating a set of infinite algebraic equations, the coefficient of the series are determined. In order to verify the validity of this method, the wave equation in a inhomogeneous medium is degenerated to the equation with constant coefficients. The domain function is discussed. The dynamic stress concentration factor around an elliptical cavity is calculated in an exponentially inhomogeneous medium.
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References
Shodja, H.M., Jarfi, H., Rashidinejad, E.: The electro-elastic scattered fields of an SH-wave by an eccentric two-phase circular piezoelectric sensor in an unbounded piezoelectric medium. Mech. Mater. 75, 1–12 (2014)
Qian, Z.H., Jin, F., Lu, T.: Transverse surface waves in an FGM layered structure. Acta Mech. 207, 183–193 (2009)
Sheikhhassani, R., Dravinski, M.: Scattering of a plane harmonic SH wave by multiple layered inclusions. Wave Motion. 51, 517–532 (2014)
Liu, Q.J., Zhao, M.J., Zhang, C.: Anti-plane scattering of SH waves by a circular cavity in an exponentially graded half space. Int. J. Eng. Sci. 78, 61–72 (2014)
Schmidt, F., Hohage, T., Klose, R., Schadle, A., Zschiedrich, L.: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain. J. Comput. Appl. Math. 218, 61–69 (2008)
Lee, J., Lee, H., Jeong, H.: Numerical analysis of SH wave field calculations for various types of a multilayered anisotropic inclusion. Eng. Anal. Bound. Elem. 64, 38–67 (2016)
Sheikhhassani, R., Dravinski, M.: Dynamic stress concentration for multiple multilayered inclusions embedded in an elastic half-space subjected to SH-waves. Wave Motion 62, 20–40 (2016)
Liu, D.K., Gai, B.Z., Tao, G.Y.: Application of the method of dynamic stress concentration. Wave Motion 4, 293–304 (1982)
Moreau, L., Caleap, M., Velichko, A., Wilcox, P.D.: Scattering of guided waves by through-thickness cavities with irregular shapes. Wave Motion 48, 586–602 (2011)
Asadi, E., Fariborz, S.J., Fotuhi, A.R.: Anti-plane analysis of orthotropic strips with defects and imperfect FGM coating. Eur. J. Mech. A Solid. 34, 12C20 (2012)
Yan, G.Z., Ye, J.G., Guo, J.: Boundary integral method for multi-layered electromagnetic scattering problems. J. Differ. Equ. 254, 4109–4121 (2013)
Liu, Q.J., Zhang, C., Todorovska, M.I.: Scattering of SH waves by a shallow rectangular cavity in an elastic half space. Soil. Dyn. Earthq. Eng. 90, 147–157 (2016)
Chen, L.: Greens function for a transversely isotropic multi-layered half-space: an application of the precise integration method. Acta Mech. 226, 3881–3904 (2015)
Daros, C.H.: Greens function for SH-waves in inhomogeneous anisotropic elastic solid with power-function velocity variation. Wave Motion 50, 101–110 (2013)
Pao, Y.H., Mow, C.C.: The Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane and Russak, New York (1973)
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Yang, Zl., Zhang, Cq., Jiang, Gxx. et al. A complex function method of SH wave scattering in inhomogeneous medium. Acta Mech 228, 3469–3481 (2017). https://doi.org/10.1007/s00707-017-1876-6
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DOI: https://doi.org/10.1007/s00707-017-1876-6