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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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