Scattering of fixed circular inclusion in right-angled plane to steady incident planar shearing horizontal wave

Complex function method and multi-polar coordinate and Fourier series expansion technology are used to study the scattering of fixed circular inclusion in right-angled plane to steady incident planar SH-wave. The incident wave and the reflection wave in the right-angled plane which has no circular inclusion are constructed; and the scattering solution excited by the boundary of the circular inclusion existing in the space, which satisfy the free stress conditions of the two right-angled boundaries are formulated, therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equation of unknown coefficients appearing in the scattering wave solution field can be gained using multi-polar coordinate transformation and Fourier series expansion technology and the conditions of displacement at the boundary of the circular inclusion. It can be solved by using limit items 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-angled plane with the variations of dimensionless wave number and the incident angle and the location of the circular inclusion. The results of the example show the effectiveness and efficiency of the method introduced here.