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Developing a Model for a Modulating Mirror Fixed on Active Supports. Deterministic Problem*

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Cybernetics and Systems Analysis Aims and scope

Abstract

We consider a problem of a modulating mirror fixed on active supports. It is assumed that the mirror may have several defects. The problem is to find optimal locations of supports and control forces that provide the best approximation of a given shape and phase of the oscillations for a homogeneous mirror as well as a plate with defects that have definite geometric and mechanical characteristics. The model of the Kirchhoff plate is chosen to describe the mirror. Defects are modeled by small inhomogeneities with changed elastic characteristics. An iterative technique for modeling finite-size defects in the Kirchhoff plate by point quadrupoles is developed. Isolated active supports are modeled by point forces. The optimization parameters are the location of the supports and the amplitudes and phases of the forces that generate vibrations. As an optimality criterion, the minimum of the root-mean-square deviation of the waveform of the plate from the given pattern is used.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    G. Zrazhevsky

  2. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    V. Zrazhevska

  3. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    O. Golodnikov

Authors
  1. G. Zrazhevsky
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  2. V. Zrazhevska
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  3. O. Golodnikov
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Corresponding author

Correspondence to G. Zrazhevsky.

Additional information

*This paper presents the results obtained in the project “Application of Buffered Probability of Exceedance (BPOE) to Structural Reliability Problems” supported by the European Office of Aerospace Research and Development. Grant EOARD #16IOE094.

Translated from Kibernetyka ta Systemnyi Analiz, No. 5, September–October, 2022, pp. 37–47.

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Zrazhevsky, G., Zrazhevska, V. & Golodnikov, O. Developing a Model for a Modulating Mirror Fixed on Active Supports. Deterministic Problem*. Cybern Syst Anal 58, 702–712 (2022). https://doi.org/10.1007/s10559-022-00503-9

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  • DOI: https://doi.org/10.1007/s10559-022-00503-9

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