<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Dynamic behaviour of contact impact forces in strongly nonlinear discontinuous vibroimpact system is studying. Contact impact force is one of the most significant vibroimpact system characteristics. We investigate the 2-DOF vibroimpact system by numerical parameter continuation method in conjunction with shooting and Newton-Raphson methods. We simulate the impact by nonlinear contact interactive force according to Hertz’s contact law. This paper is the continuation of the previous works [<xref ref-type="bibr" rid="j_AMNS.2016.1.00014_ref_001_w2aab3b7e1030b1b6b1ab2b1b1Aa">1</xref>,<xref ref-type="bibr" rid="j_AMNS.2016.1.00014_ref_002_w2aab3b7e1030b1b6b1ab2b1b2Aa">2</xref>]. We have determined the instability zones and bifurcations points for loading curves [<xref ref-type="bibr" rid="j_AMNS.2016.1.00014_ref_001_w2aab3b7e1030b1b6b1ab2b1b1Aa">1</xref>] and frequency-amplitude response [<xref ref-type="bibr" rid="j_AMNS.2016.1.00014_ref_002_w2aab3b7e1030b1b6b1ab2b1b2Aa">2</xref>] under variation of excitation amplitude and frequency. In this paper we investigate the behaviour of contact forces at bifurcation points particularly at discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump that is their moduli becoming more than unit by jump. It is phenomenon unique for nonsmooth systems with discontinuous right-hand side. We observe also the contact forces increase at <italic>nT</italic> -periodical multiple impacts regimes. We also learn the change of contact forces behaviour when the impact between system bodies became the soft one due the change of system parameters.</p></abstract>

Dynamic behaviour of contact impact forces in strongly nonlinear discontinuous vibroimpact system is studying. Contact impact force is one of the most significant vibroimpact system characteristics. We investigate the 2-DOF vibroimpact system by numerical parameter continuation method in conjunction with shooting and Newton-Raphson methods. We simulate the impact by nonlinear contact interactive force according to Hertz’s contact law. This paper is the continuation of the previous works [1,2]. We have determined the instability zones and bifurcations points for loading curves [1] and frequency-amplitude response [2] under variation of excitation amplitude and frequency. In this paper we investigate the behaviour of contact forces at bifurcation points particularly at discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump that is their moduli becoming more than unit by jump. It is phenomenon unique for nonsmooth systems with discontinuous right-hand side. We observe also the contact forces increase at nT -periodical multiple impacts regimes. We also learn the change of contact forces behaviour when the impact between system bodies became the soft one due the change of system parameters.

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Kyiv National University of Construction and Architecture

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Contact Impact Forces at Discontinuous 2-DOF Vibroimpact"}

Dynamic behaviour of contact impact forces in strongly nonlinear discontinuous vibroimpact system is studying. Contact impact force is one of the most...

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Published Online: Mar 14, 2016

Page range: 183 - 196

Received: Dec 03, 2015

Accepted: Mar 10, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00014

Keywords
vibroimpact system, discontinuous, contact force, Hertz’s law, bifurcation, multiplier, nonlinear, stability

© 2016 V.A. Bazhenov, O.S. Pogorelova, T.G. Postnikova, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Published Online: Mar 14, 2016

Page range: 183 - 196

Received: Dec 03, 2015

Accepted: Mar 10, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00014

Keywordsvibroimpact system, discontinuous, contact force, Hertz’s law, bifurcation, multiplier, nonlinear, stability

© 2016 V.A. Bazhenov, O.S. Pogorelova, T.G. Postnikova, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
vibroimpact system, discontinuous, contact force, Hertz’s law, bifurcation, multiplier, nonlinear, stability