Diffraction of acoustic waves at two-dimensional hard trilateral cylinders with rounded edges: First-order physical theory of diffraction approximation

Abstract

The paper extends the physical theory of diffraction (PTD) for finite objects with rounded edges. It started recently for objects with soft boundaries (Apaydin et al., 2017b). Here, we consider diffraction of acoustic waves at a hard trilateral cylinder. Notice that this two-dimensional acoustic problem admits electromagnetic interpretation. It is diffraction at a perfectly conducting object illuminated by a plane wave with its magnetic field vector parallel to the zaxis (Fig. 1). The acoustic surface velocity potential u can be treated as the surface electric current j (Ufimtsev, 1989, 2006, 2014). This current terminology is used in the paper. More information about PTD can be found in Ufimtsev (2013, 2009, 2014). See also the recent PTD applications for finite wedges (Rozynova and Xiang, 2017; Xiang and Rozynova, 2017). Notice as well the theoretical (Apaydin et al., 2017b) and empirical (Chambers and Berthelot, 1994) studies of sharp edges vs rounded edges. The fundamental idea of PTD is a separation of the surface currents in two components, j ¼ j PO þ j fr (Ufimtsev, 1989, 2014). The first one is the usual physical optics (PO) approximation while the second represents the diffraction/ fringe component caused by the curvature of the object surface. This component is found via solving the surface fringe integral equations (Apaydin et al., 2016b; Apaydin et al., 2017a) by the method of moments (MoM). Alternative approaches in the theory of diffraction at rounded objects and polygonal cylinders are presented in Elsherbeni and Hamid (1985), Hallidy (1985), Hamid (1973), Lucido et al. (2006), Mitzner et al. (1990), Vasiliev et al. (1991), and Yarmakhov (2004). The paper is organized as follows: Sec. II describes the geometry of the problem. In Sec. III, the integral equations for the acoustic fringe currents are formulated. Section IV presents numerical simulations. The time dependence expðixtÞ is used in the paper.