Finite‐element solution for scattering of lamb waves by asymmetrically located discontinuities in an elastic plate waveguide

This paper considers the scattering of Lamb waves due to the discontinuity of elastic plate waveguide. A method of analysis is presented which is a combination of the finite‐element method and analytical solution. The analytical solution is derived taking the cut‐off mode into consideration. Consequently, the region of application of the finite‐element method is reduced drastically compared with the traditional method of analysis by finite‐element method ignoring the cut‐off mode. In the past, the formulation has been made by restricting the discontinuities to symmetrical distribution in regard to the central plane of the plate. In this paper, this restriction is removed and discontinuities of any distribution in regard to the elastic plate can be handled. The effectiveness of taking the cut‐off mode into consideration is verified by applying the proposed method to the scattering of Lamb waves by a free‐edge of the elastic plate and by a slit which is symmetrical in regard to the central plane of the plate. As examples of discontinuities with asymmetrical distribution in regard to the central plane of elastic plate, a slit on one of the surfaces and wedge‐shaped crack are considered. The result of analysis is presented for the scattering characteristics when a fundamental symmetric Lamb wave or fundamental antisymmetric Lamb wave is incident.