Directivity and frequency property of scattering field by a penny-shaped crack

Scattering field by penny-shaped crack gains much concern in NDT. In this paper, the surface of the penny-shaped crack is regarded as pressure-released. Because it coincides with a degenerate coordinate surface of oblate spheroidal coordinate system, the separation of variable method is applied to solve the scalar wave equation to calculate scattering field. One kind of oblate angle functions, which can be expanded as the series of associated Legendre functions, is chosen as the solution of one separated differential equation. It is a solution around the ordinary point and convergent within the neighborhood area of origin. The oblate radial functions are asymptotic expansions to the solutions around the irregular singularity. They can be expressed as the series of spherical functions. The coefficients of these series are calculated by continued fraction method and normalized by properly chosen terms respectively. For the desired accuracy in numerical computation, the series are truncated according to the characteristics of asymptotic series. For normal and oblique incidence, under various kinds of conditions, the scattering field is calculated and analyzed. The directivity and low-frequency characteristics of the scattering far field on different conditions are discussed and compared with each other.