About Oscillations in Nonlinear Systems with Elastic Bonds

Abstract

This article deals with oscillations that occur with a certain combination of parameters in a nonlinear system with elastic bonds, formed by three cylinders pulled together by an elastic thread. The aim of this work was to develop a methodology for studying nonlinear oscillatory systems based on the analysis of the potential energy of a system and the balance of the forces acting on it. The novelty of the work lies in the proposed methods for determining the conditions for the occurrence of vibrations and in those for calculating the threshold value of the elasticity coefficient of an elastic thread, at which an oscillatory process is guaranteed to occur. The differential equations of oscillations were compiled and numerically solved both with and without allowance for friction forces. The critical value of the elasticity coefficient of the thread at which periodic oscillations occurred was determined. A study of the motion of the system was carried out.

Keywords

• non-linear oscillatory systems
• elastic bonds