2026

Applied Mathematical Modelling

Journal year: 2026 | Journal volume: vol. 150, part A

scientific article

english

EN We studied vibrations around a conditioned by friction stationary state in which the tip of the spring pendulum placed on a horizontal rotating disc remains at rest relative to an unmovable observer. The Amontons-Coulomb law in the two-dimensional vector formulation was used to model the frictional contact between system elements, and the discontinuous functions were approximated by second-degree Taylor polynomials. The employed approximation allows for explaining the complex role of the friction force in the dynamics of the system as not only a dissipative factor but also a restoring force in transverse vibrations and a factor responsible for asymmetric coupling. The variant of the multiple scales method (MSM) in the time domain with three variables was employed to ensure consistency with the approximation of generalised forces and preserve all terms. The asymptotic solutions were verified by quantitatively comparing them using the proposed norm in L2 space with numerical solutions, and the comparison results show that the applied MSM solves the system to a high degree of accuracy. Modulation equations of amplitudes and phases, being an inherent part of the MSM solution, were used to study the periodic resonant states, including the stability analysis. Three types of resonance response curves of the system were detected. The resonance response curves were validated by determining the amplitude of vibrations determined from numerical and asymptotic solutions. Novel nonlinear features while studying influence of the system parameters on the form of resonance response curves were reported.

116364-1 - 116364-42

10.1016/j.apm.2025.116364

https://www-1sciencedirect-1com-1sifmpo3g033f.han3.library.put.poznan.pl/science/article/pii/S0307904X2500438X

Article Number: 116364

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