Vol.4, No 16, 2004 pp. 141-156
UDC 537.226.96.(045)
A NUMERICAL APPROACH TO ANALYSIS
OF AXISYMMETRIC RINGS
Dragan Mančić, Milan Radmanović
Faculty of Electronic Engineering, University of Niš, A. Medvedeva
14, 18000 Niš, Serbia and Montenegro
E-mail: dmancic@elfak.ni.ac.yu,
radmanovic@ni.ac.yu
Abstract. In this paper, using the exact three-dimensional equations
of linear elasticity, the axisymmetric vibrations of a finite solid circular
ring of various hole and length have been studied. The real, imaginary
and complex branches of the corresponding dispersion spectra, obtained
by satisfying the stress-free boundary conditions exactly at the lateral
surface of the ring have been superposed to satisfy, approximately, the
stress-free boundary conditions at the flat surfaces of the ring. The process
of superposition yields a transcendental equation, which gives the frequency-length
curves for the ring. These curves have been given for rings with various
materials and for different selected dimensions.
Key words: Frequency equation, Numerical method, Resonance
frequency.
NUMERIČKI PRISTUP
U ANALIZI OSNOSIMETRIČNIH PRSTENOVA
U ovom radu primenom tačnih trodimenzionalnih jednačina linearne elastičnosti
analizirane su osnosimetrične oscilacije konačnih čvrstih kružnih prstenova
sa različitim otvorom i dužinom. Realne, imaginarne i kompleksne grane
odgovarajućeg disperzionog spektra, dobijene tačnim zadovoljavanjem graničnih
uslova sa nultim naponima na kružnim površinama prstena, superponirane
su da aproksimativno zadovolje granične uslove sa nultim naponima na ravnim
površinama prstena. Postupak superpozicije dovodi do transcedentne jednačine,
koja daje zavisnosti između frekvencije i dužine prstena. Ove zavisnosti
su prikazane za prstenove od različitih materijala i za različito odabrane
dimenzije.
