Transient response of thin bodies subjected to impact : Wave approach

Abstract

In this paper, we examine the problem of the response of rods, beams, plates and shells to low velocity impact. Thin bodies may possess elastic, viscoelastic, thermoelastic, isotropic, anisotropic features, as well as other features. In this paper, the emphasis is on wave theories of shock interaction. These theories are based on the fact that at the moment of impact transient waves (surfaces of strong discontinuity) are generated within the contact domain, which further propagate along the thin bodies and thereby influence the process of the shock interaction. The desired functions behind the strong discontinuity surfaces are found in terms of one-term, two-term or multiple-term ray expansions, the coefficients of which are determined with an accuracy of arbitrary functions from a set of equations describing the dynamic behavior of the thin body. On the contact domain boundary, the ray expansions for the desired functions go over into the truncated power series with respect to time and are matched further with the desired functions within the contact region that are represented by the truncated power series with respect to time with uncertain coefficients. As a result of such a procedure, it has been possible to determine all characteristics of shock interaction and, among these, to find the time dependence of the contact force and the displacements of the contact region. The proposed procedure is illustrated by numerous examples, which are combined into sections depending on the characteristics of the contact force and the dimensions of the thin bodies. The results are compared with those obtained by other approaches and procedures.