Abstract
In this paper, a class of isolation systems with rigid limiters has been considered. For this class of systems, some general discrete-time models described by means of some impact Poincaré maps have been established. Two examples: a simple isolation system of one-stage and a real isolation system of two-stages have been investigated. The calculated results show that those models can reveal complex nonlinear behaviors. And even a small random perturbation may change the dynamical character of the system.
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References
Bishop S.R. (1994). Impact oscillators. Phil Trans R Soc Lond A 347:347–351
Ibrahim, R.A., Sayad, M.A.: Nonlinear interaction of structural systems involving liquid sloshing impact loading. In: Pfeiffer, F. (ed) Proceedings of the IUTAM symposium on unilateral multibody dynamics, Munich (1998)
Bapat C.N. (1998). Periodic motions of an impact oscillator. J Sound Vib 209(1):43–60
Blazejczyk B., Kapitaniak T., Wojewoda J., Barron R. (1994). Experimental observation of intermittent chaos in a mechanical system with impacts. J Sound Vib 178:272–275
Chatterjee S., Mallik A.K. (1996). Bifurcations and chaos in autonomous self-excited oscillators. J Sound Vib 193(5):1003–1014
Gontier C., Toulemonde C. (1997). Approach to the periodic and chaotic behaviour of the impact oscillator by a continuation method. Eur J Mech A/Solids 16(1):141–163
Karyeaclis M.P., Caughey T.K. (1989a). Stability of a semi-active impact damper; part 1-Global behaviour. ASME J Appl Mech 56:926–929
Karyeaclis M.P., Caughey T.K. (1989b). Stability of a semi-active impact damper; part 2-periodic solutions. ASME J Appl Mech 56:930–940
Kozlov V.V., Treshchev D.V. (1991). Billiards. A genetic introduction to the dynamics of systems with impacts. Amer Mathematical Society, Providence (NY)
Sung C.K., Yu W.S. (1992). Dynamics of a harmonically excited impact damper: bifurcation and chaotic motion. J Sound Vib 158:317–329
Sung P.C., Shaw S.W. (1988). The dynamics of an impact print hammer. J Vib Acoust Stress Reliability Des 110:193–200
Feng Q., Pfeiffer F. (1998). Stochastic model on a rattling system. J Sound Vib 215(3):439–453
Pfeiffer F. (1988). Seltsame Attraktoren in Zahradgetrieben. Ing.-Archiv 58:113–125
Pfeiffer F., Kunert A. (1990). Rattling models from deterministic to stochastic processes. Nonlinear Dynamics 1:63–74
Pfeiffer F. (1999). Unilateral problems of dynamics. Arch Appl Mech 69(8):503–527
Brogliato B. (1999). Nonsmooth mechanics. Springer, Berlin Heidelberg New York
Delassus E. (1923). Sur les lois du frottement de glissement. Bull Soc Math fr 51:22–33
Kapitaniak T. (1988). Chaos in systems with noise. World Scientific, Singapore
Feng Q., He H. (2003). Modeling of the mean Poincaré map on a class of random impact oscillators. Eur J Mech A/Solids 22:267–281
Klotter K. (1980). Technische Schwingungslehre, Erster Band: Einfache Schwinger, Teil B: Nichtlinear Schwingungen. Springer, Berlin Heidelberg New York
Bell D.J., Cook P.A., Munro N. (1982). Design of moden control systems. Peter Peregrinus Ltd, New York
Ibrahim R.A. (1985). Parametric random vibration. Wiley, New York
Wang Y., Feng Q., Wang Q.Y. (2004). Study on mathematical models of anti-shock isolation system of a marine engine. J Ship Mech 8(3):124–132
He, H.: The two-stage isolation system with limiters under shock excitation. Tong Ji University Dissertation (2005).
Moon F.C. (1987). Chaotic vibrations. An introduction for applied scientists and engineers. Wiley, New York
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Feng, Q. Discrete Models of a Class of Isolation Systems. Arch Appl Mech 76, 277–294 (2006). https://doi.org/10.1007/s00419-006-0026-8
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DOI: https://doi.org/10.1007/s00419-006-0026-8