Dynamic Response of a Pre-Stressed Transversely Isotropic Plate to Impact by an Elastic Rod

This article considers the problem of normal impact of a long thin elastic cylindrical rod upon an infinite pre-stressed elastic transversely isotropic plate possessing cylindrical anisotropy. The impact takes place at the center of the plate, whose equations of motion take both rotary inertia and shear deformations into account. During the shock interaction of the rod with the plate, waves with strong discontinuities are generated in the plate and begin to propagate. Behind the fronts of these waves, the solution is constructed in terms of ray series, the coefficients of which are the different order discontinuities in partial-time derivatives of the desired functions, and the time elapsed after the wave arrival at the point (of the plate) under consideration is a variable. The ray series coefficients are determined from recurrent equations within the accuracy of arbitrary constants, which are determined from the conditions of the dynamic contact interaction between the impactor and the target. These arbitrary constants allow one to construct the solution both within and outside the contact region. It is shown that as the radial compression forces reach a critical magnitude, the velocity and amplitude of the transient wave of transverse shear both diminish to zero. This leads us to the fact that the portion of the impact energy that is expended in work performed by transverse forces is completely absorbed at the contact spot, resulting in the occurrence of a damaged area within the contact region.