UDC 519.9
3 V.M. Glushkov Institute of Cybernetics of NAS of Ukraine,Kyiv, Ukraine
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DEVELOPING A MODEL FOR MODULATING MIRROR FIXED ON
ACTIVE SUPPORTS. DETERMINISTIC PROBLEM
Abstract. We consider a problem of a modulating a mirror fixed on active supports. It is assumed that the mirror may have several defects.
The problem is to find optimal locations of supports as well as control forces providing 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 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.
Keywords: modulating mirror, defected plate, optimal excitation.
FULL TEXT
REFERENCES
- Zrazhevsky G., Golodnikov A., Uryasev S. Mathematical methods to find optimal control of oscillations of a hinged beam (deterministic case). Cybernetics and Systems Analysis. 2019. Vol. 55, N 6. P. 1009–1026. https://doi.org/10.1007/s10559-019-00211-x .
- Zrazhevsky G., Zrazhevska V. Formulation and study of the problem of optimal excitation of plate oscillations. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics. 2019. Vol. 1. P. 62–65. https://doi.org/10.17721/1812-5409.2019/1.12.
- Khludnev A.M. On thin inclusions in elastic bodies with defects. Z. Angew. Math. Phys. 2019. Vol. 70, Iss. 2. Article 45. https://doi.org/10.1007/s00033-019-1091-5.
- Zrazhevsky G., Zrazhevska V. Usage of generalized functions formalism in modeling of defects by point singularity. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics. 2019. Vol. 1. P 58–61. https://doi.org/10.17721/1812-5409.2019/1.12 .
- Zrazhevsky G., Zrazhevska V. Modeling of finite inhomogeneities by discrete singularities. Journal of Numerical and Applied Mathematics. 2021. Vol. 1 (135). P. 138–143. https://doi.org/10.17721/2706-9699.2021.1.18 .
- Zrazhevsky G., Zrazhevska V. The extension method for solving boundary value problems of theory of oscillations bodies with heterogeneity. World Journal of Engineering Research and Technology. 2020. Vol. 6, Iss. 2. P. 503–514.
- Donnell LH. Beams, plates, and shells. New York: McGraw-Hill Book Company, 1976. 453 p.
- Lawson C.L., Hanson R.J. Solving least square problems. Englewood Cliffs, NJ: Prentice-Hall, 1974. 524 p.
- AORDA Portfolio Safeguard (PSG). URL: http://www.aorda.com.
