Application of the Recursive Transfer Method to Flexural Waves I: Novel Discretization Scheme Using Weak Form Theory Framework and Waveguide Modes on Inhomogeneous Elastic Plates

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Flexural waves on a thin elastic plate are governed by the fourth-order differential equation, which is attractive not only from a harmonic analysis viewpoint but also useful for an efficient numerical method in the elastdynamics. In this paper, we proposed two novel ideas: (1) use of the tensor bases to describe flexural waves on inhomogeneous elastic plates, (2) weak form discretization to derive the second-order difference equation from the fourth-order differential equation. The discretization method proposed in this study is of preliminary consideration about the recursive transfer method (RTM) to analyse the scattering problem of flexural waves. More importantly, the proposed discretization method can be applied to any system which can be formulated by the weak form theory. The accuracy of the difference equation derived by the proposed discretization method is confirmed by comparing the analytical and numerical solutions of waveguide modes. As a typical problem to confirm the validity of the resultant governing equation, the influence of the spatially modulated elastic constant in waveguide modes is discussed.

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