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Autoresonant homeostat concept for engineering application of nonlinear vibration modes

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A Publisher's Erratum to this article was published on 13 February 2007

Abstract

Analysis of strongly nonlinear (vibro-impact) systems revealed an existence of nonlinear modes of vibration with spatial and temporal concentration of energy. The modes can be realised, for example, through intensification of the vibration process by condensing the vibration into a sequence of collisions for impulsive action of the tools to the media being treated or can be as a result of some discontinuity (slackening of a contact, arrival of crack, etc.) in the structure. The use of the nonlinear modes to develop useful mechanical work leads to necessity of excitation and control of resonance in ill-defined dynamical systems. This is due to the poorly predictable response of the media being treated. Excitation, stabilisation and control of a nonlinear mode at the top intensity in such systems is an engineering challenge and needs a new method of adaptive control for its realisation.

Such a control technique was developed with the use of self-exciting mechatronic systems. The excitation of the nonlinear mode in such systems is a result of artificial instability of mechanical system conducted by positive electronic feedback. The instability is controlled by intelligent identification of the mode and active tracing of the optimal relationship between phase shifting and limitation in the feedback circuitry. This method of control is known as autoresonance. Applications of autoresonant control for development of the new machines are described.

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Authors and Affiliations

  1. Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Leicestershire, UK

    V. I. Babitsky & I. J. Sokolov

Authors
  1. V. I. Babitsky
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  2. I. J. Sokolov
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Correspondence to V. I. Babitsky.

Additional information

The paper is a revised and extended version of authors’ presentation at ASME 2004 International Mechanical Engineering Congress, Anaheim, CA, USA.

An erratum to this article can be found at http://dx.doi.org/10.1007/s11071-007-9239-9

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Babitsky, V.I., Sokolov, I.J. Autoresonant homeostat concept for engineering application of nonlinear vibration modes. Nonlinear Dyn 50, 447–460 (2007). https://doi.org/10.1007/s11071-006-9181-2

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  • DOI: https://doi.org/10.1007/s11071-006-9181-2

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