Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 2, 2016 (June)
Pages 25-30
Cited by J. of Mech. Eng., 2016, vol. 19, no. 2, pp. 25-30



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

T. P. Raimberdiyev, Akhmet Yassawi International Kazakh-Turkish University (29, B. Sattarkhanov Ave, Turkestan, Kazakhstan)

E. M. Shekhvatova, National Aerospace University “KhAI” (17, Chkalov St., Kharkov, 61070, Ukraine)



To describe the vibrations of a beam with a transverse crack, a quasilinear dynamical system with a finite number of degrees of freedom is obtained. To obtain this system, the solution was decomposed according to the forms of linear oscillations. The Galerkin method was applied to partial differential equations describing the vibrations of a beam with a crack. Nonlinear dynamical systems with two and three degrees of freedom with internal resonances were analyzed. In a quasilinear dynamical system, subharmonic vibrations in the region of the second main resonance were studied using the method of multiple scales.


Keywords: vibrations of a beam with a breathing crack, Bubnov-Galerkin method, finite degrees of freedom dynamical system, method of multiple scales, principle resonance)



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Received 01 February 2016

Published 30 June 2016