Modeling of the oscillation amplitude of a statically indeterminate flat frame subjected to the impact load with account taken of the contact deformation

Abstract

Introduction. The article addresses transverse vibrations of a post in a rigidly fixed statically indeterminate flat frame subjected to the falling load, having pre-set mass and pre-impact velocity. The post of a vertical frame has initial curvature affecting the maximum amplitude of transverse vibrations triggered by the impact. Materials and methods. In the course of modeling, the frame beam impact takes account of deformations in the contact area to ensure the accuracy of calculations, because otherwise the impact force value will be overestimated. It is assumed that the falling load has the shape of a cylinder featuring a certain length, when the transverse load impact on a frame beam is simulated. The linearization of the relationship between the force and the deformation of cylindrical surfaces is used. The frame post, connected to the beam and the base, is a homogeneous rod rigidly fixed at both ends. Following the load impact on the frame beam, the top end of the post absorbs the initial bending moment and the shear force, whose values depend on the mass the and pre-impact velocity of the load, the beam attachment method, and the ratio between axial moments of inertia in beam and post sections in the plane of the frame. Using the method of initial parameters, the maximum deflection of a perfectly straight and curved post is calculated for different pre-impact velocity values of the load. The maximum deflection was modeled for curved and perfectly straight posts at different pre-impact velocities of a load having the same mass. Results. The dependence between the value of maximum deflection of a vertical frame post and the pre-impact velocity of the falling load was obtained.