Application of parameter continuation method for analysis of vibroimpact 2-dof systems

Authors

  • Ольга Семеновна Погорелова Kyiv National University of Construction and Architecture, Povitroflotsky Avenue 31, Kyiv, 03680, Ukraine https://orcid.org/0000-0002-5522-3995
  • Татьяна Георгиевна Постникова Kyiv National University of Construction and Architecture, Povitroflotsky Avenue 31, Kyiv, 03680, Ukraine https://orcid.org/0000-0002-6677-4127
  • Валентина Владимировна Отрашевская Kyiv National University of Construction and Architecture, Povitroflotsky Avenue 31, Kyiv, 03680, Ukraine https://orcid.org/0000-0001-9879-1442

DOI:

https://doi.org/10.15587/.2014.27939

Keywords:

vibroimpact system, parametric continuation method, periodic solutions, Hertzian contact force, parameterization, arc length, stability, multiplier

Abstract

The possibility and peculiarities of the numerical parameter continuation method application to the mechanical system with repeating impacts are considered. The theoretical bases of the continuation method combined with the shooting method and Newton-Raphson method are presented. The technique is adapted to two-mass two-degree-of-freedom vibroimpact system under periodic excitation. The peculiarities and difficulties of the technique application to vibroimpact systems, i.e. mechanical systems, which constantly change their structure due to repeating impacts among their elements are discussed. Parameterization is fulfilled after the arc length of the solution curve that allows to pass turning points and find branch points. The impact is simulated by nonlinear contact interaction force based on the quasistatic Hertzian contact theory, which takes into account local deformations of colliding bodies in the contact zone. Such simulation allows to obtain the law of motion of bodies on the whole time base, including impact period. It also allows to calculate the impact forces, which are the significant characteristics of vibroimpact motion. It can be successfully applied to systems with soft impact that is confirmed by experiments. Stability or instability of periodic solutions is determined by monodromy matrix eigenvalues (multipliers) based on the Floquet theory. The values of multiplies, the module of which is greater than one, are defined by the types of bifurcation points.

Author Biographies

Ольга Семеновна Погорелова, Kyiv National University of Construction and Architecture, Povitroflotsky Avenue 31, Kyiv, 03680

Candidate of Physico-mathematical Sciences, Senior Research Officer

Scientific Research Institute of Structural Mechanics

Татьяна Георгиевна Постникова, Kyiv National University of Construction and Architecture, Povitroflotsky Avenue 31, Kyiv, 03680

Candidate of Engineering Sciences, Senior Researcher

Scientific Research Institute of Structural Mechanics

Валентина Владимировна Отрашевская, Kyiv National University of Construction and Architecture, Povitroflotsky Avenue 31, Kyiv, 03680

Candidate of Physico-Mathematical Sciences, Associate Professor

Department of Higher Mathematics 

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Published

2014-10-02

How to Cite

Погорелова, О. С., Постникова, Т. Г., & Отрашевская, В. В. (2014). Application of parameter continuation method for analysis of vibroimpact 2-dof systems. Technology Audit and Production Reserves, 5(3(19), 11–15. https://doi.org/10.15587/.2014.27939

Issue

Vol. 5 No. 3(19) (2014): Fundamental and applied researches: integration into the world scientometric databases

Section

Mathematical Modeling - Applied Aspects

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Copyright (c) 2016 Ольга Семеновна Погорелова, Татьяна Георгиевна Постникова, Валентина Владимировна Отрашевская

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