Numerical Modeling of Elastic Waves in a Semi-Infinite Thin Plate

Numerical modeling of thin-shell structures allows saving the calculation resources by replacing relatively simple three-dimensional models on heavy numerical grids with lighter grids and more complex shell or plate models that comprise the behavior of the material through the thickness of a plate. Different shell and plate models consider different processes or states, and this research is dedicated to a particular dynamic model that considers the propagation of elastic waves in a medium that is limited by two planar free borders. The application of this model involves low-amplitude vibrations and ultrasound propagation in thin-shell structures. The approach used in this research is based on the dynamic Kirchhoff–Love model that is reduced to a system of hyperbolic equations that is solved with the grid-characteristic numerical method. Hyperbolic properties of the equations system allow to form a description for a full set of elastic waves that can propagate in a thin-shell structure, including bending edge waves. The numerical model of the free border is verified qualitatively on three-dimensional calculations for similar statements that were performed with a previously verified implementation of the grid-characteristic method for three-dimensional elasticity.