Possibilities of Using Frequency Energy Functions in Problems of Dynamics of Machines for Transport and Technological Purposes

Andrey Eliseev,Roman Bolshakov,Sergey Eliseev,Nikolay Kuznetsov,S Bratan,S Roshchupkin

doi:10.1051/matecconf/202134603073

Abstract

New approaches to the evaluation of the dynamic properties of mechanical vibration systems are proposed, which consider as the design schemes for technical objects operating under dynamic vibration loads. The purpose of the study is to develop ideas for the use of frequency energy functions. In this case, the frequency functions represent the ratio of the potential and kinetic energies in a specific form, based on the use of the relations of the coordinates of the system in the stationary mode. The technologies of system analysis and structural mathematical modeling are used. In this approach, the mechanical oscillatory system is correspond with the block diagram of the automatic control system, which is equivalent in dynamic terms. It is proposed to use the analytical apparatus to take into account the features of interpartial relations, to evaluate the specific modes of dynamic interaction of system elements. A method for determining the natural vibration frequencies of the system based on the use of the frequency energy function is proposed. Methodological bases of approaches to solving problems of system dynamics related to the assessment of the influence of system parameters on their frequency properties are developed. The results of computational modeling are presented.

Highlights

Many technical objects of transport and technological purposes are operated in conditions of increased dynamic loads
It is shown that the design schemes of technical objects, displayed by the design schemes in the form of mechanical oscillatory systems, allow us to detail the ideas about the dynamic properties associated with the assessment of the dynamic states of objects determined by the spectrum of natural vibration frequencies in a wide range
A method for estimating the dynamic properties of mechanical oscillatory systems based on the introduction of the concept of the frequency energy function is proposed

Summary

Introduction

Many technical objects of transport and technological purposes are operated in conditions of increased dynamic loads. Https://doi.org/10.10 51/matecconf /202134603073 scientific and methodological basis for solving the problem of the dynamics of machines, equipment and mechanisms operating under periodic (most often harmonic) external influences of a power or kinematic nature In this connection, attention is justified to the features of dynamic properties that can be reflected using the frequency characteristics of systems. The determination of the natural vibration frequencies of systems involves the construction of mathematical models based on analytical or approximate approaches, which is usually used in engineering practice [10, 11].At the same time, there is a need for more detailed estimates of the frequency properties of mechanical oscillatory systems, which in analytical approaches encounters certain difficulties Interesting ideas in this direction were proposed by Rayleigh [12]. The proposed report reflects a scientific and methodological approach that allows us to consider the frequency properties of mechanical oscillatory systems in a fairly generalized form and evaluate the possible forms of influence of the system parameters on the natural frequencies of its free oscillations

Some general provisions

Conclusion