*Article* **Analytical Study of SH Wave Scattering by a Circular Pipeline in an Inhomogeneous Concrete with Density Variation**

**Zailin Yang 1, Chenxi Sun 1, Guanxixi Jiang 2, Yunqiu Song 1, Xinzhu Li <sup>1</sup> and Yong Yang 1,\***


**\*** Correspondence: yangyongheu@163.com

**Abstract:** In this paper, the shear horizontal (SH) wave scattering by a circular pipeline in an inhomogeneous concrete with density variation is studied. A model of inhomogeneous concrete with density variation in the form of a polynomial-exponential coupling function is established. By using the complex function method and conformal transformation, the incident and scattering wave field of SH wave in concrete are obtained, and the analytic expression of dynamic stress concentration factor (DSCF) around the circular pipeline is given. The results show that the inhomogeneous density parameters, the wave number of the incident wave and the angle of the incident wave in concrete are important factors affecting the distribution of dynamic stress around the circular pipe in concrete with inhomogeneous density. The research results can provide a theoretical reference and a basis for analyzing the influence of circular pipeline on elastic wave propagation in an inhomogeneous concrete with density variation.

**Keywords:** inhomogeneous concrete; SH wave; circular pipeline; complex function method; dynamic stress concentration factor
