Dynamic Loading of Bar Systems with a Finite Number of Degrees of Freedom

The study of the stability of systems with a finite number of degrees of freedom under the influence of dynamic loads is an important problem of structural mechanics. Such systems are widely used in mechanical systems in various fields: construction, mechanical engineering, aircraft construction, shipbuilding, instrument engineering, and biomechanics. In case of seismic impacts, it is necessary to check the building’s structural elements for dynamic stability. The issue of determining the critical state of systems with a finite number of degrees of freedom under dynamic loads is solved in this paper. The article presents a method for analyzing the dynamic stability of bar systems with one and two degrees of freedom. Bar systems with a finite number of degrees of freedom, which are subjected to a dynamic compressive load in the longitudinal direction, are considered. In the hinges, the bars are connected by elastic springs that counteract the instability of the system. To solve the problem, ordinary differential equations are composed. One equation is composed for a single-degree-of-freedom system and a system of two equations for a three-bar system (a two-degree-of-freedom system). The obtained equations allow to study the stability of a system with a finite number of degrees of freedom. Numerical method is used to solve the problem. Numerical integration of the equations is performed by the Runge - Kutta method. Based on the calculation results, graphs of the relationships between the deflection of the bar systems and the acting dynamic load are constructed. The change in the “ t 1 time” shows the value of the dynamic coefficient k д. The influence of the parameter of the rate of change of the compressive load and the initial imperfection on the criteria of dynamic stability of bar systems with one and two degrees of freedom is investigated.