Studying dynamics of machine-building structure rod elements

Abstract

The purpose of the work is to study the dynamic processes of cantilever rods with several degrees of freedom on the basis of an accurate analytical method of forces. On the basis of corresponding matrix operations the initial rod system with two dynamic degrees of freedom is reduced to a simplified system of equations with a single degree of freedom. This significantly reduces the volume and complexity of computational operations. A harmonic vibration load simulating the action of unbalanced rotating masses is taken as an external influence. The calculation of free oscillations on the basis of the theory of eigenvalues and vectors has allowed to obtain the expressions for circular frequencies of natural oscillations as well as to build the eigenforms of oscillations in the shape of “standing" waves. The calculation of constrained oscillations has resulted in receiving the numerical values of mass dynamic movements under different ratios of the circular frequencies of constrained and free oscillations. It has been found that the period of constrained oscillations decreases monotonically with the increase of the frequency ratio while the amplitudes of mass oscillations remain sufficiently stable. The analytical dependences proposed in this study will find wide application in solving rod system dynamic problems in mechanical and civil engineering, aircraft construction and shipbuilding.