Two approaches in the analytical investigation of the spring pendulum

• Autorzy: Sypniewska-Kamińska G. , Starosta R. , Awrejcewicz J.
• Języki publikacji: EN

Abstrakty

EN

Dynamics of the nonlinear spring pendulum is analysed using two asymptotic approaches. The multiple scale method is commonly applied with using two time scales. The purpose of the research is to justify the introduction of an additional third scale. Results of the analysis clearly show that introducing the third scale improve correctness of the approximate analytical solution. The obtained results allow for qualitative and quantitative analysis of the behavior of the studied system with a high accuracy. Calculations are made both in the neighbourhood of the resonance and also far from it.

Słowa kluczowe

EN

nonlinear dynamics; asymptotic method; spring pendulum

PL

dynamika nieliniowa; metoda asymptotyczna; wahadło sprężynowe

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2018
• Tom: Vol. 29
• Strony: art. no. 2018005
• Opis fizyczny: Bibliogr. 9 poz., 1 rys., wykr.

Twórcy

autor

Sypniewska-Kamińska G.

• Poznan University of Technology, Institute of Applied Mechanics ul. Jana Pawła II 24, 60-965 Poznań, Poland

autor

Starosta R.

• Poznan University of Technology, Institute of Applied Mechanics ul. Jana Pawła II 24, 60-965 Poznań, Poland

autor

Awrejcewicz J.

• Technical University of Łódź, Department of Automatics and Biomechanics, ul. Stefanowskiego 90-924, Łódź, Poland

Bibliografia

• 1. R. Starosta, G. Sypniewska-Kamińska, J. Awrejcewicz, Parametric and external resonances in kinematically and externally excited nonlinear spring pendulum, IJBC, 21(10) (2011) 3013 - 3021.
• 2. R. Starosta, G. Sypniewska-Kamińska, J. Awrejcewicz, Asymptotic analysis of kinematically excited dynamical systems near resonances, Nonlinear Dynamics, 68(4) (2012) 459 - 469.
• 3. J. Awrejcewicz, R. Starosta, G. Sypniewska-Kamińska, Asymptotic analysis of resonances in nonlinear vibrations of the 3-dof pendulum. Differ. Equ. Dyn. Syst. 21(1&2) (2013) 123 - 140.
• 4. J. Awrejcewicz, G. Kudra, G. Wasilewski, Chaotic zones in triple pendulum dynamics observed experimentally and numerically, Mechanics and Materials 9 (2008) 1 - 17.
• 5. K. Furuta, T. Ochiai, N. Ono, Attitude control of a triple inverted pendulum. International Journal of Control, 39 (1984) 1351 - 1365.
• 6. I. Fantoni, R. Lozano, M. W. Spong, Energy based control of the pendubot. IEEE Transactions on Automatic Control, AC-45 (2000) 725 - 729.
• 7. D. Sado, K. Gajos, Analysis of vibrations of three-degree-of-freedom dynamical system with double pendulum. J. of Theoretical and Applied Mechanics, 46(1) (2008) 141 - 156.
• 8. A. H. Nayfeh, Perturbation Methods. Wiley, New York 1973.
• 9. B. K. Shivamoggi, Perturbation Method for Differential Equations, Birkhauser, Boston 2002.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).