In the paper the vibrations of the complex mechanical system in non-stationary state have been analysed. The characteristics feature of the system is that all masses move along straight line and each of them, apart from the exreme ones, interacts only with neighbouring one. The interaction forces are ninlinearly dependent on displacements and relative velocities. The system in question is a model of the freight train motion during braking process. The particular masses are effected by the external forces with delayed argument, which is related to the time when the braking wave reaches the particular carrieges. The set of 40, 50 and 60 masses has been considered, in particular. It has been found out that independly on the mass number, the middle masses have the maximum values of vibration amplitudes. These amplitudes increase with the increase of the mass number. Solutions of the linearised and non-linear systems are compared. The influence damping on the system vibration has been examined.
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The problem of self-excited and non-linear parametric vibration occurring in cold strip rolling processes is analysed. The mathematical model of oscillated system is given: the sequence of the rolling stands coupled by transferring strip. The approximate analytical solution and the results of the calculations for some parameters of the rolling strip are presente
Praca przedstawia przybliżoną analizę na podstawie prostego modelu drgań masztu wzmocnionego odciągami. Drgania te wywoływane są odrywaniem się od masztu wirów Karmana. Wykazano, że zjawisko drgań ma charakter samowzbudno-parametryczny. W pracy zamieszczono charakterystyki amplitu-dowo-częstotiiwościowe, amplitudowo-fazowe oraz przebiegi czasowe drgań uzyskane dzięki analizie numerycznej.
EN
The paper presents an approximate analysis based on a simple model of vibrations of a mast supported by stay cables. The vibrations of the mast are excited by the separation of the Karman vortex. It has been demonstrated that the vibrations in the discussed structure has the self-excited parametric character. The paper includes the frequency and phase characteristics well as the time plots obtained by means of numerical analysis.
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