Propagation of elastic waves in a finite-sized body subjected to the Instantaneous concentrated force impact

Abstract

The article proposes a method for solving the spatial problem of the propagation of elastic vibrations in a circular plate of limited dimensions under an instantaneous concentrated vertical surface force impact $Q$, which consists in finding the components of the displacement vector for each point of the body as a function of space and time. The problem arose in the process of predicting the residual resource of dangerous metal structures by the acoustic emission method, which uses circular piezoelectric sensors and requires the determination of resonance conditions during wave propagation.