The Modeling of Mechanical Engineering Facilities to Reduce the Impact of External Vibration Effects

Abstract

The article considers free and forced oscillations of a system with six degrees of freedom with symmetrical and asymmetrical mass-inertial characteristics. The conditions of single-frequency oscillations are obtained. Initial deviations and initial velocities must be interconnected through one of the amplitude distribution coefficients. The differential equations of free vibrations of the system in principal coordinates are six independent linear differential equations of second order. Their common solution is obtained. We examine the possibility of reduction in the quantity of degrees of freedom of the considered system from six to two ones. Passing from six degrees of freedom to two was substantiated with the aid of the numerical experiments. According to calculations, linear and angular deflections of the transportation vehicle, which has six and two degrees of freedom, differ not more than by 10%. This fact indicates that it is possible to replace a study of a system with six degrees of freedom with a system with two degrees of freedom. An example of the transport system, which has three degrees of freedom, is considered. The obtained differential equation is solved in the final form with the specific relationship of the parameters. Analogously, there are equations derived and solutions obtained for the systems, which have one, one-and-ahalf and two degrees of freedom. The equations obtained allow you to define transformations of right parts depending on the considered case of external influences applied to the system and on the number of degrees of freedom. Keywords—mechanical engineering; vibration effects; modeling; forced oscillations; mass-inertial characteristics