On the Modeling of the Oscillating Process of Longitudinal Elastic Body by Two-Point Problem

Abstract

The oscillating process of an elastic one-dimensional longitudinal body like bar with known values of the body position at two moments of time is described by the problem with conditions two-point in time for partial differential equations. Modification of the mathematical model has allowed to distinguish the class of quasi-polynomials, in which the corresponding problem has an unique solution. A method of constructing an exact solution is proposed. Examples of models of some systems are given and the oscillation processes in them are investigated.