A note on the mathematical model of machine vibration

• Autorzy: Olach Rudolf , Chupáč Radoslav , Dorociaková Božena
• Języki publikacji: EN

Abstrakty

EN

In the article, we investigate the stability of a simple mathematical model describing the vibration of a machine. The model is characterized by a nonlinear second-order differential equation with a delay. We present a detailed stability analysis and examination of the equilibrium of this equation, providing insights into the dynamic behavior of the system. The aim of the article is to investigate the effect of body movement on equilibrium stability and to determine the value of the parameter at which body vibration occurs. The research used a methodology for solving the given type of nonlinear differential equations, for example, linearization.

Słowa kluczowe

EN

mathematical model; differential equation; vibration; periodic motion

PL

model matematyczny; równanie różniczkowe; drgania; ruch okresowy

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 3
• Strony: 54--62
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Olach Rudolf

• Department of Applied Mathematics, University of Žilina Žilina, Slovak Republic

autor

Chupáč Radoslav

• Department of Applied Mathematics, University of Žilina Žilina, Slovak Republic

autor

Dorociaková Božena

• Department of Applied Mathematics, University of Žilina Žilina, Slovak Republic

Bibliografia

• 1. Beards, C.F. (1995). Engineering Vibration with Application to Control Systems. Elsevier.
• 2. Johnson, M., & Moon, F.C. (1999). Experimental characterization of quasiperiodicity and chaos in a mechanical system with delay. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 9, 49-65.
• 3. Kalmár-Nagy, T., Stépán, G., & Moon, F.C. (2001). Subcritical hopf bifurcation in the delay equation model for machine tool vibrations. Nonlinear Dyn. Syst. Theory, 26, 121
• 4. Beards, C.F. (2015). Engineering Vibration Analysis with Application to Control Systems. Edward Arnold.
• 5. Liu, L., & Yang, Y. (2015). Modeling and Precision Control of Systems with Hysteresis. Butterworth-Heinemann
• 6. Ying, P., Tang, H., Chen, L., Ren, I., & Kumer, A. (2023). Dynamic modeling and vibration characteristics of multibody system in axial piston pump. Alexandria Engineering Journal, 62, 523-540.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).