Application of the reciprocity principle to evaluation of mode-converted scattered shear horizontal (SH) wavefields in tapered thinning plates.

The interaction of guided waves with wall thinning can be complex, depending on the thinning geometry and the frequency. At a high frequency-thickness, when a shear-horizontal (SH) guided wave mode impinges upon a tapered wall thinning region, there is mode conversion to other propagating SH modes, either in reflection or transmission, which heavily depends on the shape of the taper. In this paper, we have combined the reciprocity theorem of elastodynamics and the theory of multiple reflections, in order to analytically calculate the scattered SH wavefield in plates, due to the interaction with an arbitrary tapered thinning. The taper is discretized into several sections and the formulation is addressed in matrix notation, in order to tackle several modes which arise due to mode interconversion distributed within the taper. The method was validated with experimental and numerical data at linear tapered thinning, in the high-frequency-thickness regime. It was also applied to provide understanding of the reflection behaviour within smoother taper profiles, namely, raised-cosine and Blackman window tapers, and to visualize the propagating field of each mode. It is shown that for a linear taper profile, the reflection within the taper is virtually constant, which produces an interference pattern in the overall reflection from the whole taper. Such a mechanism is broken with smoother tapers, since they impose lower reflection close to the taper ends. The method proves itself useful for analytically investigating the scattering from arbitrary wall thinning when mode-conversion arises.