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Abstract
In this paper, for the case of gas oscillator two characteristic thermodynamic change of state, and for them defined functional dependence of the force from moving the piston in a nonlinear form were considered. In this paper small oscillations are observed and the linearization is performed by neglecting nonlinear term as the small size at isothermal change and with development obtained function in Taylor series for adiabatic change. Based on the analysis of analog oscillator of mechanical system, or the equivalent scheme of problems, characteristics oscillation parameters and the motion law of the observed thermodynamic system are defined. With this procedure greatly simplifying for problem solution was achieved with respect to classical procedure. At the end of the paper, an analysis of the obtained results were done and appropriate electrical analogy was setting. This is used for the presentation of the problem through appropriate electric circuits and analogy mathematical relations, which involve voltage and electric currents as electric sizes. Also, it was shown that the electrical analogy can be used for all mechanical and thermodynamic processes which describes by homogeneous second-order differential equations which are the most common in technical practice.
Highlights
Rezultujuća sila koja dejstvuje na klip i koja teži da ga vrati u ravnotežni položaj biće: F = F ' '−F ' = A ⋅ p' '− A ⋅ p' = A( p''− p' ) (5)
Brzina kretanja klipa za oba slučaja može se dobiti diferenciranjem jednačina kretanja (44) i (50)
With this procedure greatly simplifying for problem solution was achieved with respect to classical procedure
Summary
Posmatrajmo zatvoreni cilindar poprečnog preseka A = D2π , gde je D-unutrašnji prečnik cilindra, u čijoj se unutrašnjosti nalazi klip mase m zanemarljive širine u odnosu na prečnik i dužinu cilindra, sl.. Kada se klip nalazi na sredini cilindra, u položaju x=0, pritisak gasa na obe strane klipa je p0, što predstavlja. Adresa autora: Branko Pejović, Univerzitet u Istočnom Sarajevu, Tehnološki fakultet, Zvornik, Karakaj bb. Trenje izmeñu klipa i cilindra biće zanemareno. Pod pretpostavkom da su oscilacije klipa oko ravnotežnog položaja male, odredićemo jednačinu ovog oscilatornog kretanja kao i parametre oscilovanja za slučaj dve karakteristične promene stanja gasa: izotermsku i adijabatsku. Možemo pretpostaviti da se u cilindru nalazi vazduh. Radi jednostavnijeg dobijanja rešenja, koristićemo mehaničku analogiju dok će se predstavljanje problema izvršiti električnom analogijom, preko odgovarajućih ekvivalentnih kola. Slika 1 - Gasni oscilator sa karakterističnim veličinama za proračun: a) početno stanje, b) proizvoljni položaj
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