Study of the Influence of Boundary Motion on the Oscillatory and Resonance Properties of Mechanical Systems with Variable Length
https://doi.org/10.23947/2587-8999-2025-9-2-34-43
Abstract
Introduction. The widespread use of technical systems with moving boundaries necessitates the development of mathematical modelling methods and algorithmic software for their analysis. This paper presents a systematic review of studies examining the oscillatory and resonance properties of mechanical systems with moving boundaries, such as hoisting cables, flexible transmission mechanisms, strings, rods, beams with variable length, and others.
Materials and Methods. A problem statement is formulated, and numerical methods are developed for solving nonlinear problems that describe wave processes and the resonance properties of systems with moving boundaries.
Results. An analysis is conducted on wave reflection from moving boundaries, including changes in their energy and frequency. It is shown that the energy of the system increases when the boundary moves toward the waves and decreases when moving in the same direction as the waves. Criteria are obtained to determine the conditions under which the boundary motion must be considered for accurate calculation of oscillation amplitudes. Numerical results demonstrate the influence of boundary speed and damping on the system dynamics.
Discussion and Conclusion. The findings have practical significance for the design and operation of mechanical systems with variable geometry. The results make it possible to prevent large-amplitude oscillations in mechanical objects with moving boundaries at the design stage. These problems have not been sufficiently studied and require further research
About the Authors
A. L. Semenov
Lomonosov Moscow State University
Russian Federation
Russian Federation
Aleksey L. Semenov, Academician of the Russian Academy of Sciences, Academician of the Russian Academy of Education, Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics
119991, GSP-1, Moscow, Leninskie Gory
V. L. Litvinov
Samara State Technical University
Russian Federation
Russian Federation
Vladislav L. Litvinov, Candidate of Technical Sciences, Head of the Department of General Theoretical Disciplines (Higher Mathematics)
443100, Samara, Molodogvardeyskaya St., 244
M. V. Shamolin
Lomonosov Moscow State University
Russian Federation
Russian Federation
Maksim V. Shamolin, Corresponding Member of RAS, Doctor of Physical and Mathematical Sciences, Professor, Leading Researcher at the Laboratory of General Mechanics, Research Institute of Mechanics
119991, GSP-1, Moscow, Leninskie Gory
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Review
For citations:
Semenov A.L., Litvinov V.L., Shamolin M.V. Study of the Influence of Boundary Motion on the Oscillatory and Resonance Properties of Mechanical Systems with Variable Length. Computational Mathematics and Information Technologies. 2025;9(2):34-43. https://doi.org/10.23947/2587-8999-2025-9-2-34-43
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