Vol.1, No 2, 1997 pp. 65 - 72
UDC:534.64

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DYNAMICS OF THE DUFFING OSCILLATOR WITH IMPACTS
Slavka Mitić
Faculty of Occupational Safety, University of  Niš
Čarnojevića 10a, 18000 Niš, Yugoslavia; fax: +381 18 49962

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Abstract. Single degree of freedom system, which is described with the Duffing differential equation, with rigid arrester was studied on the basis of the non-linear systems theory and stereo-mechanical impact theory. The impact vibrations in Duffing oscillator subjected to harmonics excitation in the case of the unilateral rigid arrester and in the case of the symmetrical bilateral arrester were determined numerically by approximate method Runge - Kutta of the fourth order. Turbo pascal programs were composed and the computer graphics was used. The qualitative analyses of the global dynamic stability of the non-linear impact systems having unilateral or symmetrical bilateral arrester was carried out on the basis of phase portraits and of two-dimensional mapping.
Key words: vibroimpact motion, unilateral and symmetrical rigid arrester, stereo-mechanical impact theory, phase portrait, two dimensional mapping.

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DINAMIKA DUFFING-OVOG OSCILATORA SA UDARIMA Oscilatorni sistem sa jednim stepenom slobode, opisan Duffing-ovom diferencijalnom jednačinom, sa krutim ograničivačem, izučavan je na osnovu nelinearne teorije i stereomehaničke teorije udara. Udarne oscilacije Duffing-ovog oscilatora, sa harmonijskom pobudom, u slučaju jednostranog krutog ograničivača i u slučaju simetričnog dvostranog krutog ograničivača, odredjene su numerički pomoću metode Runge-Kutta četvrtog reda. Sastavljeni su odgovarajući Turbo-pascal programi i korišćena je kompjuterska grafika. Kvalitativna analiza globalne dinamičke stabilnosti nelinearnih udarnih sistema sa jednostranim ili sa simetričnim dvostranim ograničivačem sprovedena na osnovu faznih portreta i dvodimenzionih mapa.