Development of software that applies artificial intelligence methods to model and analyze vibrations and resonance effects in mechanical systems with changing boundaries

This article presents the TB-ANALYSIS software package developed for intelligent analysis and control of resonance dynamics in one-dimensional systems with moving boundaries. Implemented in the MATLAB environment, the package combines classical methods for solving boundary value problems (analytical, asymptotic, and approximate) with artificial intelligence (AI) technologies to predict and prevent resonance phenomena. A key feature of the development is its hybrid architecture, which, along with numerical modeling and factor analysis modules, implements an intelligent module based on deep neural networks (DNNs). This module automatically predicts resonant frequencies based on model parameters and determines optimal values for damping, viscoelasticity, and stiffness coefficients to suppress resonance. Neural networks are trained using synthetic data generated by the package itself. The effectiveness and accuracy of the package have been confirmed by testing on model problems.