The features of solutions of dynamical systems with an external exciting load and non-conservative dynamical systems with pairwise interaction of degrees of freedom

Abstract

When mathematical models are developed, as a rule, a number of assumptions is done, which makes it possible to simplify the model, reduce its dimension and simulation time, or use the dimension reduction method. When modeling non-conservative systems with pairwise interaction of degrees of freedom, e.g. mechatronic systems, an elastic aircraft in a flow, an aeroelastic aircraft with an automated control system, etc., there is a desire to reduce the problem to a conservative dynamic system with harmonic action. The study shows that despite the apparent similarity of the tasks, they have significant differences that cannot be ignored. Differences in the behavior of conservative dynamical systems and non-conservative dynamical systems with pair interaction of degrees of freedom are considered. The results are demonstrated on the simplest example with an analytical solution, and in the finite element software package MSC.Nastran. The results of the solution in MSC.Nastran are compared with the results of the analytical solution.