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Control Problem of String Vibrations with Inseparable Multipoint Conditions at Intermediate Points in Time

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Abstract

The problem of controlling the vibrations of a string with given inseparable values of the deflection function and velocities at intermediate times is considered. By the method of separation of variables, the problem reduces to the problem of controlling ordinary differential equations with given initial, final, and unseparated multipoint intermediate conditions. The problem is solved using methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions. As an application of the proposed approach, a control action is constructed for the control problem of string vibrations with specified unseparated conditions on the values of the deflection function and string velocities at two intermediate points in time.

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Authors and Affiliations

  1. Yerevan State University, Alex Manoogian 1, Yerevan, 375025, Republic of Armenia

    V. R. Barseghyan

  2. Institute of Mechanics, National Academy of Sciences of Republic of Armenia, Marshal Baghramian ave. 24b, Erevan, 0019, Republic of Armenia

    V. R. Barseghyan

Authors
  1. V. R. Barseghyan
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Correspondence to V. R. Barseghyan.

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Russian Text © The Author(s), 2019, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2019, No. 6, pp. 108–120.

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Barseghyan, V.R. Control Problem of String Vibrations with Inseparable Multipoint Conditions at Intermediate Points in Time. Mech. Solids 54, 1216–1226 (2019). https://doi.org/10.3103/S0025654419080120

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  • DOI: https://doi.org/10.3103/S0025654419080120

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