Abstract
A mathematical model of the one-dimensional controlled motion of a hybrid vibrational system is proposed. The plant includes an inhomogeneous elastic rod with loads concentrated at its endpoints. An analytical-numerical procedure for finding the eigenvalues (eigenfrequencies) and eigenfunctions is developed. A novel procedure to take into account the nonuniform distributed forces and forces concentrated at the endpoints using a modification of Grinberg’s approach is presented. Efficient statements and constructive approximate solutions of the problems for controlling the motion of a countably dimensional vibrational system with a complex distribution of eigenfrequencies are proposed.
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Original Russian Text © L.D. Akulenko, A.A. Gavrikov, 2018, published in Izvestiya Akademii Nauk, Teoriya i Sistemy Upravleniya, 2018, No. 3, pp. 5–14.
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Akulenko, L.D., Gavrikov, A.A. Controlling the One-Dimensional Motion of Hybrid Vibrational Rod Systems. J. Comput. Syst. Sci. Int. 57, 349–357 (2018). https://doi.org/10.1134/S1064230718020028
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DOI: https://doi.org/10.1134/S1064230718020028