Cybernetics and Systems Analysis

, Volume 55, Issue 6, pp 1009–1026 | Cite as

Mathematical Methods to Find Optimal Control of Oscillations of a Hinged Beam (Deterministic Case)*

  • G. ZrazhevskyEmail author
  • A. Golodnikov
  • S. Uryasev


We consider several problem statements for the optimal controlled excitation of oscillations of a hinged beam. Oscillations occur under the influence of several external periodic forces. In the simplest statement, it is assumed that the structure of the beam is homogeneous. In a more complex formulation, inhomogeneities (defects) on the beam are allowed. The goal of controlling the oscillations of the beam is to provide a predetermined shape and a predetermined pointwise phase of oscillations in a given frequency range. The problem is to determine the number of forces and their characteristics (application, amplitude, and phase of oscillations), which provide the desired waveform with a given accuracy. With the help of analytical mathematical methods, the problems in question are reduced to simpler multiextremum problems of minimizing basic functionals, which can be numerically solved using the multifunctional package AORDA PSG.


vibrations waveform optimal actuation 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine
  2. 2.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  3. 3.University of FloridaGainesvilleUSA

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