Modeling of the Maximum Deflection of a Stepped Rod Having an Initial Curvature Upon Impact Against a Rigid Barrier

The solution of dynamic problems of the longitudinal impact of a homogeneous rod in a nonlinear formulation presents, notoriously, significant mathematical difficulties. Existing approaches have a rather limited application mainly due to the significant approximation of the solution of the problem. In addition, such approaches affect an extensive mathematical apparatus, which complicates their use in engineering calculations. The task of solving the problem of the longitudinal impact of a geometrically heterogeneous (stepped) rod remains far from the final solution to this day. The solution of this problem is complicated by the randomness of the interference pattern of longitudinal waves during their transition through the boundaries of homogeneous sections of a stepped rod, and therefore the deformations and longitudinal forces along the length of the rod quickly change in time. In this work, using the initial parameter method and the wave model of longitudinal impact, an attempt is made to develop a methodology for calculating the dynamic deflection of a stepped rod that performs transverse vibrations during a longitudinal impact on a rigid barrier. The value of the maximum deflection of a stepped rod with the initial curvature of one of its sections is modeled. The results of modeling the maximum deflection for various values of the initial curvature and the pre-impact speed of the rod are obtained. During the processing of simulation results, the so-called “Zone of maximum deflections” is the interval of variation of the pre-shock velocity, at which the maximum amplitude of the transverse vibrations of the curved section of the stepped rod is observed. The possibility of calculating the amplitudes of the transverse vibrations of the rods and rod elements under the most various fixing schemes and the various nature of the pre-shock state is noted. The relevance of applying this technique in dynamic calculations of various impact mechanisms, as well as in engineering calculations of rod systems for various purposes, is emphasized.