Scattering of fixed half circular inclusion at boundary of a right-angle planar space to steady incident planar SH-wave

Complex function method, multi-polar coordinate and Fourier series expansion technology are used here to study scattering of fixed half circular inclusion located at horizontal boundary of a right-angular planar space to steady incident planar SH-wave. At first, incident wave and reflection wave in the right-angular planar space which has no circular inclusion are constructed; then the scattering solution excited by the boundary of the fixed circular half inclusion, which satisfies the free stress conditions of the two right-angle boundaries, is formulated. Therefore, the total displacement field can be constructed using superposition principle. An infinite set of algebraic equations of unknown coefficients appearing in the scattering wave solution field can be gained using multi-polar coordinate transformation, Fourier series expansion technology and the conditions of displacement at the boundary of the fixed half circular inclusion. It can be solved by using limit terms in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the displacement ratio and the phase of the displacement on the horizontal boundary of the right-angle planar space vs the variations of dimensionless wave numbers and the incident angles and the different locations of the fixed half circular inclusion. The example results show the effectiveness and feasibility of the method proposed.