Recent trends in asymptotical techniques with applications to mechanics

• Autorzy: Awrejcewicz J.
• Języki publikacji: EN

Abstrakty

EN

Three important problems of mechanics are addressed. The first corresponds to analytical prediction of a suitable choice of a delay loop parameters in order to control a transitional (perturbed) behaviour of a periodic vibro-impact process modelled by one degree-of-freedom system. The second presents an application of the Melnikov's method to stick-slip chaos prediction in periodically driven self-excited oscillator. The third one illustrates an application of a so called „small 5 method” to analysis of strong non-linear oscillations using example of a mathematical pendulum.

Słowa kluczowe

EN

vibro-impact processes; stick-slip; strongly non-linear systems; asymptotic analysis

PL

procesy drganiowo-uderzeniowe; stick-slip; układy silnie nieliniowe; analiza asymptotyczna

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2000
• Tom: Vol. 19
• Strony: 34--46
• Opis fizyczny: Bibliogr. 13 poz., wykr.

Twórcy

autor

Awrejcewicz J.

• Katedra Automatyki i Biomechaniki, Politechnika Łódzka, ul. Stefanowskiego 1/15, 90-924 Łódź

Bibliografia

• [1] Andrianov I.V., Awrejcewicz J.: New Trends in Asymptotic Approaches. Part I. Summation and Interpolation Methods (to appear).
• [2] Awrejcewicz J., Tomczak К., Lamarque C.-H.: Controlling Systems With Impacts, International Journal of Bifurcation and Chaos, Vol. 9,No. 3 (1999), 547-553.
• [3] Awrejcewicz J., Andrianov I.V., Manevitch L.I.: Asymptotic Approach in Nonlinear Dynamics: New Trends and Applications, Springer-Verlag, Berlin 1998.
• [4] Awrejcewicz J., Holicke M.: Melnikov’s Method and Stick-Slip Chaotic Oscillations in Very weakly Forced Mechanical Systems, International Journal of Bifurcation and Chaos, Vol. 9, No. 3 (1999), 505-518.
• [5] Awrejcewicz J., Andrianov I.V.: Methods of Small and Large S in the Nonlinear Dynamics-А Comparative Analysis (to appear).
• [6] Awrejcewicz J.: Bifurcation and Chaos in Simple Dynamical Systems, World Scientific, Singapore 1989.
• [7] Awrejcewicz J.: Bifurcation and Chaos in Coupled Oscillators, World Scientific, Singapore 1991.
• [8] Awrejcewicz J.: Synchronization and Chaos, Łódź TU Press, Łódź 1995, in Polish.
• [9] Awrejcewicz J.: Asymptotic Methods - a New Perspective of Knowledge, Łódź TU Press, Łódź 1995, in Polish.
• [10] Awrejcewicz J.: Secrets of Nonlinear Dynamics, Łódź TU Press, Łódź 1997, in Polish.
• [11] Awrejcewicz J.: Oscillations of Discrete Deterministic Systems, Wydawnictwo Naukowo-Techniczne, Warsaw 1996, in Polish.
• [12] Awrejcewicz J. (ed.): Bifurcation and Chaos: Theory and Application, Springer Verlag, Heidelberg, New York 1995.
• [13] Awrejcewicz J. (ed.): Nonlinear Dynamics: New Theoretical and Applied Results, Akademie Verlag, Berlin 1995.