A software package for predicting and analyzing oscillatory processes in mechanical systems with moving boundaries

A software package for predicting and analyzing oscillatory processes in mechanical systems with moving boundaries

Litvinov V.L. (SamGTU, Samara, Russia)
Shamolin M.V. (MSU, Moscow, Russia)
Litvinova K.V. (MSU, Moscow, Russia)

Abstract

The study of the dynamics of objects with moving boundaries described by one-dimensional boundary value problems is of significant interest for modern engineering and scientific calculations. The article presents the developed software package "TB-ANALYSIS", created in the MATLAB environment for mathematical modeling and analysis of the resonant characteristics of objects with moving boundaries. A key feature of the package is the integration of classical numerical methods with modern artificial intelligence algorithms. To solve boundary value problems, three main methods are implemented: an analytical method for replacing variables in a system of functional-difference equations, an asymptotic method, and an approximate method for constructing solutions to integro-differential equations. Intelligent selection of the method is carried out automatically depending on the type of the problem being solved. The system's architecture includes interconnected modules accessible through a single graphical interface. The main modules are designed to investigate solutions to boundary value problems, analyze resonance properties, and control resonance phenomena. To ensure calculation accuracy, a special error estimation procedure is implemented at each step. To demonstrate the system's capabilities, a study was conducted on the transverse vibrations of a variable-length viscoelastic cable resting on an elastic foundation. The study focuses on the use of artificial intelligence, neural networks, and machine learning to analyze resonance phenomena, predict optimal system parameters, and prevent resonance. The use of deep neural networks and adaptive control increased the accuracy of predictions and the effectiveness of system control. As a result, the neural network can predict resonant frequencies and suggest optimal parameters. Calculations confirmed that the parameters suggested by the artificial intelligence do indeed prevent resonance. The developed software package is an effective tool for studying the dynamics of objects with moving boundaries. Prospects for further development include expanding the class of problems solved and implementing additional numerical methods.

Keywords

software package; moving boundaries; boundary value problems; resonance phenomena; artificial intelligence; machine learning; neural networks; MATLAB; vibrations of one-dimensional objects; parameter optimization; variable-length systems.

Edition

Proceedings of the Institute for System Programming, vol. 38, issue 2, 2026, pp. 269-286

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2026-38(2)-18

For citation

Litvinov V.L., Shamolin M.V., Litvinova K.V. A software package for predicting and analyzing oscillatory processes in mechanical systems with moving boundaries. Proceedings of the Institute for System Programming, vol. 38, issue 2, 2026, pp. 269-286 DOI: 10.15514/ISPRAS-2026-38(2)-18.

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