Vol.5, No 1, 2006 pp. 25 - 41
UDC 534.1:534.012:534.013:
THE FREQUENCY EQUATION THEOREMS OF SMALL
OSCILLATIONS OF A
HYBRID SYSTEM CONTAINING COUPLED DISCRETE AND CONTINUOUS SUBSYSTEMS
Katica (Stevanović) Hedrih
Faculty of Mechanical Engineering University of Niš, 18000 Niš, Vojvode
Tankosića 3/22,
e-mail: katica@masfak.ni.ac.yu
/ khedrih@eunet.yu,Telefax: +381
18 241-663
Abstract. In this paper, by using examples of hybrid systems of
a dynamically coupled discrete subsystem of rigid bodies and continuous
subsystem, the method for obtaining frequency equations of small oscillations
is presented. Also, a theorem of small oscillations frequency equations
is defined. By using examples, analogy between frequency equations of some
classes of these systems is identified. Special cases of discretization
and continualization of coupled subsystems in the light of these sets of
proper circular frequencies and frequency equations of small oscillations
are analyzed. The set of the frequency equation theorems of small oscillations
of the hybrid system containing coupled discrete and continuous subsystems
are defined.
Key words: Hybrid systems, coupled subsystems, rigid bodies,
continuous, elastic body, frequency equation, theorem.
TEOREME O FREKVENTNIM JEDNAČINA MALIH
OSCILACIJA HIBRIDNIH SISTEMA,
KOJI SADRŽE SPREGNUTE DISKRETNE I KONTINUALNE PODSISTEME
Koristeći primer hibridnog sistema sastavljenog od dinamički spregnutih
podsistema krutih tela i kontinualnog podsistema, postavljena je metoda
dobijanja frekventnih jednačina malih oscilacija hibridnih sistema. Takodje
je postavljeno nekoliko teorema koje definišu osobine frekventnih jednačina
posmatrane klase hibridnih sistema. Koristeći primere i analogiju izmedju
nekih klasa hibridnih sistema pokazana je analogija izmedju njihovih frekventnih
jednačina. Specijalni slučajevi diskretizacije i kontinualizacije spregnutih
podsistema u odnosu na njihove skupove sopstvenih kružnih frekvencija i
frekventnih jednačina malih oscilacija su proučeni. Izveden je i dokazan
skup teorema o frekventnim jednačinama je malih oscilacija hibridnih sistema
koji se sadrže, dinamičkim vezama spregnute diskretne i kontinualne podsisteme.
Ključne reči: Hibridni system, spregnuti podsistemi, kruta tela,
deformabilna tela, frekventne jednačine, teoreme.
