Simulation of Tthe Amplitude of Transverse Oscillations of the Rod System upon Impact of a Falling Load, Taking into account Deformation in the Contact Area

Abstract

The oscillatory process of a rod system of arbitrary shape under shock interaction with a falling load is considered. The system may consist of a large number of rods connected to each other rigidly or pivotally, and striking is assumed to be one of the core elements, thus causing a complex oscillatory process. As an example, vibrations of a rigidly sealed statically indeterminate flat two-post frame experiencing a drop of a load of a given mass and pre-impact velocity are simulated. One of the vertical pillars of the frame has an initial curvature, the presence of which affects the maximum amplitude of transverse vibrations arising from impact. The impact of the load on the frame crossbar is modeled taking into account the deformation in the contact area, which is justified from the point of view of the accuracy of the calculations, because otherwise the magnitude of the impact force will be overestimated. When modeling the impact interaction of the load and the rod system under consideration, it is assumed that the falling load has the shape of a cylinder with a certain length of the generatrix. Linearization of the relationship between force and deformation of cylindrical surfaces is used. The proposed method of modeling the amplitude of transverse oscillations makes it possible to further study the characteristics of the oscillatory process depending on the mass of the falling load and its pre-impact velocity, as well as on the configuration of the rod system. The relevance of the work for calculations of structural elements of various purposes experiencing impact is emphasized, since the presented model can be used for engineering calculations of a wide class of core systems.