Regular and chaotic dynamics of a 4-DOF mechanical system with dry friction

• Autorzy: Kosińska A. , Awrejcewicz J. , Grzelczyk D.
• Konferencja: Symposium Vibrations In Physical Systems (27 ; 09-13.05.2016 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

In this paper the model of four degree-of-freedom mechanical sliding system with dry friction is considered. One of the components of the mentioned system rides on driving belt, which is driven at constant velocity. This model corresponds to a row of carriage laying on a guideway, which moves at constant velocity with respect to the guideway as a foundation. From a mathematical point of view the analyzed problem is governed by four second order differential equations of motion, and numerical analysis is performed in Mathematica software. Some interesting behaviors are detected and reported using Phase Portraits, Poincaré Maps and Lyapunov Exponents. Moreover, Power Spectral Densities obtained by the Fast Fourier Transform technique are reported. The presented results show different behaviors of the system, including periodic, quasi-periodic and chaotic orbits.

Słowa kluczowe

EN

periodicity; quasiperiodicity; chaos; hyperchaos; non-regular vibrations

PL

okresowość; quasi-okresowość; chaos; hiperchaos; drgania nieliniowe

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2016
• Tom: Vol. 27
• Strony: 195--202
• Opis fizyczny: Bibliogr. 5 poz., 1 rys., wykr.

Twórcy

autor

Kosińska A.

• Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, 1/15 Stefanowski Street, 90-924 Lodz

autor

Awrejcewicz J.

• Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, 1/15 Stefanowski Street, 90-924 Lodz

autor

Grzelczyk D.

• Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, 1/15 Stefanowski Street, 90-924 Lodz

Bibliografia

• 1. J. Abdo, M. Tahat, A. Abouelsoud, M. Danish, The effect of frequency of vibration and humidity on the stick–slip amplitude, International Journal of Mechanics and Materials in Design, 6 (2010) 45 – 51.
• 2. D. Grzelczyk, J. Awrejcewicz, G. Kudra, Dynamics of mechanical sliding system with dry friction, Machine Dynamics Research, 38(3) (2014) 61 – 70.
• 3. A. Kosińska, J. Awrejcewicz, D. Grzelczyk, Dynamics of two coupled 4-DOF mechanical linear sliding systems with dry friction, Dynamical Systems - Control and Stability, Eds. J. Awrejcewicz, M. Kaźmierczak, J. Mrozowski, P. Olejnik, TU of Lodz, Lodz, ( 2015 ) 327 – 340 (978-83-7283-708-0).
• 4. J. A. C. Martins, J. T. Oden, F.M.F. Simoes, A study of static and kinetic friction. International Journal of Engineering Science, 28(1) (1990) 29 – 92.
• 5. J. Awrejcewicz, P. Olejnik, Analysis of dynamics systems with various friction laws, Applied Mechanics Reviews, 58(6) (2005) 389 – 411.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.