Development of a method for computer simulation of a swinging spring load movement path

Authors

DOI:

https://doi.org/10.15587/1729-4061.2019.154191

Keywords:

pendulum oscillations, periodic paths of movement, swinging spring, Lagrange equation of the second kind

Abstract

Studies of geometric modeling of non-chaotic periodic paths of movement of loads attached to a variety of mathematical pendulums were continued. Pendulum oscillations in a vertical plane of a suspended weightless spring which maintains straightness of its axis were considered. In literature, this type of pendulum is called a swinging spring. The sought path of the load of the swinging spring was modeled with the help of a computer using values of the load weight, stiffness of the spring and its length without load. In addition, initial values of oscillation of the swinging spring were used: initial angle of deviation of the spring axis from the vertical, initial rate of change of this angle as well as initial parameter of the spring elongation and initial rate of elongation change. Calculations were performed using Lagrange equation of the second kind. Variants of finding conditionally periodic paths of movement of a point load attached to a swinging spring with a movable fixing point were considered.

Relevance of the topic was determined by necessity of study and improvement of new technological schemes of mechanical devices which include springs, in particular, the study of conditions of detuning from chaotic oscillations of the elements of mechanical structures and determination of rational values of parameters to ensure periodic paths of their oscillation.

A method for finding values of a set of parameters for providing a nonchaotic periodic path of a point load attached to a swinging spring was presented. The idea of this method was explained by the example of finding a periodic path of the second load of the double pendulum.

Variants of calculations for obtaining periodic paths of load movement for the following set parameters were given:

‒ length of the spring without load and its stiffness at an unknown value of the load weight;

‒ length of the spring without load and the value of the load weight at unknown spring stiffness;

‒ value of the load weight and stiffness of the spring at an unknown length of the spring without load.

As an example, determination of the values of a set of parameters to provide a non-chaotic, conditionally periodic path of movement of a point load attached to a swinging spring with a movable attachment point was considered.

Phase paths of functions of generalized coordinates (values of angles of deflection of the swinging spring axis from the vertical and extension of the spring) were constructed with the help of which it is possible to estimate ranges of these values and rates of their variation.

The results can be used as a paradigm for studying nonlinear coupled systems as well as in calculating variants of mechanical devices where springs affect oscillation of their elements when it is necessary to detune from chaotic movements of loads in the technologies using mechanical devices and provide periodic paths of their movement

Author Biographies

Leonid Kutsenko, National University of Civil Defense of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Doctor of Technical Sciences, Professor

Department of Engineering and Rescue Technology

Oleg Semkiv, National University of Civil Defense of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Doctor of Technical Sciences, Vice-Rector

Department of Prevention Activities and Monitoring

Andrii Kalynovskyi, National University of Civil Defense of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD, Associate Professor

Department of Engineering and Rescue Technology

Leonid Zapolskiy, Ukrainian Civil Protection Research Institute Rybalska str., 18, Kyiv, Ukraine, 01011

PhD, Senior Researcher

Department of Scientific and Organizational

Olga Shoman, National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Professor, Head of Department

Department of Geometrical Modeling and Computer Graphics

Gennadii Virchenko, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» Peremohy ave., 37, Kyiv, Ukraine, 03056

Doctor of Technical Sciences, Associate Professor

Department of Descriptive Geometry, Engineering and Computer Graphics

Viacheslav Martynov, Kyiv National University of Сonstruction and Architecture Povitroflotskyi ave., 31, Kyiv, Ukraine, 03037

Doctor of Technical Sciences, Associate Professor

Department of Architectural Constructions

Maxim Zhuravskij, National University of Civil Defense of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD

Department of Educational and Methodical

Volodymyr Danylenko, National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkiv, Ukraine, 61002

Associate Professor

Department of Geometrical Modeling and Computer Graphics

Nelli Ismailova, Military Academy Fontanska doroha str., 10, OdesSa, Ukraine, 65009

Doctor of Technical Sciences, Associate ProfessorDepartment of Engineering Mechanics

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Published

2019-01-14

How to Cite

Kutsenko, L., Semkiv, O., Kalynovskyi, A., Zapolskiy, L., Shoman, O., Virchenko, G., Martynov, V., Zhuravskij, M., Danylenko, V., & Ismailova, N. (2019). Development of a method for computer simulation of a swinging spring load movement path. Eastern-European Journal of Enterprise Technologies, 1(7 (97), 60–73. https://doi.org/10.15587/1729-4061.2019.154191

Issue

Vol. 1 No. 7 (97) (2019): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2019 Leonid Kutsenko, Oleg Semkiv, Andrii Kalynovskyi, Leonid Zapolskiy, Olga Shoman, Gennadii Virchenko, Viacheslav Martynov, Maxim Zhuravskij, Volodymyr Danylenko, Nelli Ismailova

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