Universal Algorithm for Generation of Matrices Used in Dynamics of Circular Thimoshenko Segments
The paper deals with a numerical generation of the basic solutions for a set of ordinary differential equations governing the plane vibration of a circular Timoshenko segment and having the normal Cauchy's form. The generation algorithm arose as further development of author's method described in [1] and enables to analyse the stationary harmonic motion of the segment for any boundary conditions and arbitrary values of physical parameters. Numerical calculations are restricted to the analysis of simply supported segments only. For testing purposes, however, this analysis is performed for three types of models: Rayleigh-Timoshenko (RT) and Bernoulli - Euler models with extensible (BEe) or inextensible (BEi) axis. The results of eigenfrequency calculations are plotted and tabulated.
References
B.OLSZOWSKI, Free in-plane vibrations of unsupported circular rings. Part I. Natural frequencies, Rozpr. Inż., 37, 3, 547-563, 1989; Part II. Natural modes, Rozpr. Inż., 38, 3-4, 529-547, 1990; Part III. Free single-frequency vibrations, Rozpr. Inż., 38, 3-4, 549-565, 1990,
V.KOLOUŠEK, Dynamics in engineering structures, Butterworths, London 1973.
B.AKESSON, H.TAGNFORS and O.JOHANNESSON, Beams and frames in bending vibration [in Swedish], Almqvuist and Wiksell, Stockholm 1972.
B.ÅKESSON and H.TÄGNFORS, PFVIBAT – A computer program for plane frame vibration analysis, Publ. No. 25, Chalmers Univ. of Technol., Div, of Solid Mech., Gothenburg 1974.
H.WITTRICK and F.W.WILLIAMS, A general algorithm for computing natural frequencies of elastic structures, Q.J. Mech. Appl. Math., 24, 263-284, 1971.
R.LUNDEN and B. ÅKESSON, Damped second-order Rayleigh-Timoshenko beam vibration in space – an exact complex dynamic member stiffness matrix, Int. J. Num. Meth. Engng., 19, 3, 431-449, 1983.
P.O.FRIBERG, Coupled vibrations of beams – an exact dynamic element stiffness matrix, Int. J. Num. Meth. Engng. 19, 479-493, 1983.
P.O.FRIBERG, Beam element matrices derived from Vlasov's theory of open thinwalled elastic beams, Div. of Solid Mech., Chalmers Univ. of Technol., Gothenburg 1984,
M.S.ISSA, T.M.WANG and B.T.HSIAO, Extensional vibrations of continuous circular curved beams with rotary inertia and shear deformation, I. Free vibration, J. Sound and Vibr., 114, 2, 297-308, 1987.
T.M.WANG and M.S.ISSA, Extensional vibrations of continuous circular curved beams with rotary inertia and shear deformation, II. Forced vibration, J, Sound and Vibr., 114, 2, 309-323, 1987.
И.И.ГОЬДЕНБЛАТ, А.М.СИЗОВ, Справочник по расчету строительных конструкций на устойчивость и колебания, Гос. Изд. Литер. по Строит. и Арх., Москва 1952.