Resonance subharmonic vibrations of beam with breathing fatigue crack

Authors

  • К. В. Аврамов Institute of Problems of Mechanical Engineering. AN Podgorny NAS, Ukraine
  • Т. П. Раимбердиев International Kazakh-Turkish University Haji Ahmed Yasavi, Kazakhstan
  • E. М. Шехватова National Aerospace University. NE Zhukovsky "Kharkiv Aviation Institute", Ukraine

Keywords:

vibrations of beam with breathing crack, Galerkin method, finite degree of freedom dynamical system, multiple scales method, principle resonance

Abstract

The vibrations of the beam with breathing crack are described by the partial differential equation with contact parameter. The quasi linear dynamical system with finite degrees of freedom is obtained to analyze the beam vibrations. In order to obtain this dynamical system the solution is expanded by eigenmodes. The Galerkin method is applied to the partial differential equation, which is described the beam vibration. It is shown, when the stiffness matrix of the beam with crack is symmetric and when it is asymmetric. The multiple scales method is used to analyze the quasilinear dynamical system. The considered dynamical system contains the internal resonance. The second main resonance is analyzed. The system of four autonomous differential equations is obtained. The characteristic exponents of the linearized modulation equations are calculated to analyze stability of the periodic motions. The frequency response at the second principal resonance is obtained. This frequency response describes the system subharmonic vibrations

Author Biographies

К. В. Аврамов, Institute of Problems of Mechanical Engineering. AN Podgorny NAS

Doctor of Technical Sciences

Т. П. Раимбердиев, International Kazakh-Turkish University Haji Ahmed Yasavi

Doctor of Technical Sciences

References

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Y. C. Chu, M.-H. H. Shen. Analysis of forced bilinear oscillators and the application to cracked beam dynamics. AIAA Journal. Vol. 30. p. 2512–2519 (1992)

T. G. Chondros, A. D. Dimarogonas, J. Yao. A continuous cracked beam vibration theory. J. of Sound and Vibr. Vol. 215. p. 17-34 (1998)

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Published

2016-06-16

Issue

Vol. 19 No. 2 (2016)

Section

Dynamics and Strength of Machines

License

Copyright (c) 2016 К. В. Аврамов, Т. П. Раимбердиев, E. М. Шехватова

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