The scattering characteristics of non‐confocal elliptical lined tunnels under SH‐wave disturbance are investigated. The problem is essentially a boundary value problem and its theoretical treatment is based on the wave function expansion method, which is an exact treatment of the problem. Multi‐elliptic co‐ordinate systems are employed and wave function translations between multi‐elliptic co‐ordinate systems are performed using the extra‐domain addition theorem of the Mathieu function. The method can be used to fit and handle scattering problems with a wide range of geometries by varying the minor‐and‐major axis ratio, lining thickness and relative position of the tunnel. Calculations have been performed on the truncated infinite linear equation established by considering the boundary conditions. Based on the calculation results a parametric study is carried out to analyze the effect of the dimensionless eccentricity distance, the minor‐and‐major axis ratio and the dimensionless wave number on the dynamic stresses around the tunnel. Two typical application examples of concrete lining in granite and steel lining in granite are presented.
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