Controlling the One-Dimensional Motion of Hybrid Vibrational Rod Systems
- Authors: Akulenko L.D.1, Gavrikov A.A.1
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics
- Issue: Vol 57, No 3 (2018)
- Pages: 349-357
- Section: Control in Deterministic Systems
- URL: https://journals.rcsi.science/1064-2307/article/view/220105
- DOI: https://doi.org/10.1134/S1064230718020028
- ID: 220105
Cite item
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.
About the authors
L. D. Akulenko
Ishlinsky Institute for Problems in Mechanics
Email: gavrikov@ipmnet.ru
Russian Federation, Moscow, 119991
A. A. Gavrikov
Ishlinsky Institute for Problems in Mechanics
Author for correspondence.
Email: gavrikov@ipmnet.ru
Russian Federation, Moscow, 119991