NON-LINEAR NORMAL FORMS OF FORCED OSCILLATIONS OF PIECEWISE LINEAR SYSTEMS AT SUPER-HARMONIC RESONANCES

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J. of Mech. Eng., 2017, vol. 20, no. 4, pp. 24-30

DOI:   https://doi.org/10.15407/pmach2017.04.024

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 20, no. 4, 2017 (December)
Pages 24–30

 

Authors

B. V. Uspenskiy, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine)

K. V. Avramov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail:  kvavramov@gmail.com, ORCID: 0000-0002-8740-693X

O. Ya. Nikonov, Kharkiv National Automobile and Highway University (25, Yaroslava Mudrogo St, Kharkiv, 61002, Ukraine)

 

Abstract

A method for calculating forced oscillations of essentially non-linear piecewise linear systems at super-harmonic resonances is proposed. The basis of this method is a combination of non-linear normal forms and the Rauscher method, by which a non-autonomous dynamic system is reduced to an equivalent autonomous system. With the help of the proposed method, super-harmonic oscillations are investigated in the power train section of an internal combustion engine. Properties of resonant oscillations are considered in detail.

 

Keywords: super-harmonic resonances, Rauscher method, non-linear normal forms, configuration space

 

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Received 23 October 2017