Keywords: flexural edge wave, asymptotic model, wave speed, bending moment, shear force, deflection, rotation angle..

In this paper we consider a flexural wave localized near the edge of thin isotropic semi-infinite plate. It is well-known that flexural edge waves are not explicitly described by original equations of motion within the classical Kirchhoff theory. We present a new methodology of highlighting the flexural edge wave contribution into the overall displacement field of the plate. Our approach is based on a recently developed one for surface waves. Within the aforementioned methodology, we consider an isotropic thin semi-infinite plate governed by Kirchhoff theory. The free edge of the plate is loaded with two types of non-stationary edge forces: by bending moment and shear force, normal to the mid-surface of plate. The exact solutions for plate deformation are expressed in terms of Fourier and Laplace integral transforms. Such solutions have poles corresponding to flexural edge wave contribution. Derivation of constant coefficient of flexural edge wave speed allows to simplify a problem and to avoid complications based on dispersive nature of such wave. It also makes it possible to analyse asymptotically the exact solutions near the poles corresponding to flexural edge wave speed. This allows construction of the approximate equations which describe the wave propagation. The model consists of two-dimensional elliptic problem corresponding to edge wave decay over the interior domain of the plate and one-dimensional fourth-order beam-like parabolic equation extracting contribution of flexural edge wave propagation into the plate deformation along the edge. The aforementioned model reveals a dual parabolic-elliptic nature of the wave under study and extracts its contribution into the whole dynamic response.

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