Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation

摘要

The paper is concerned with a bending edge wave on a thin orthotropic elastic plate resting on a Winkler--Fuss foundation. The main focus of the contribution is on derivation of a specialised reduced model accounting for the contribution of the bending edge wave to the overall dynamic response, allowing simplified analysis for a number of dynamic problems. The developed formulation includes an elliptic equation associated with decay over the interior, and a beam-like equation on the edge governing wave propagation accounting for both bending moment and modified shear force excitation, thus highlighting a dual parabolic-elliptic nature of the bending edge wave. A model example illustrates the benefits of the approach.