Abstract
The paper deals with Rayleigh-Timoshenko and Bernoulli-Euler models of circular arches with extensible or inextensible axes clamped with free radial sliding at both ends. The general algebraic equation defining the eigenproblem has been derived from Hamilton's principle. Spectral properties of the models were analysed by means of the classical Rayleigh-Ritz approximation method. Eigenfrequencies as functions of the subtending angle of the arch are plotted and tabulated.
References
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H.BARUH, S.S.K. TADIKONDA, Another look at admissible functions, J. Sound Vibr., 132, 1, 73-87, 1989.
B.OLSZOWSKI, Free in-plane vibrations of unsupported circular rings. Part I. Natural frequencies [in Polish], Engng. Trans., 37, 3, 547-563, 1989; Part II. Natura/modes [in Polish], Engng. Trans., 38, 3-4, 185-202, 1990; Part III. Free single Frequency vibrations [in Polish], Engng. Trans., 38, 3-4, 203-219, 1990.
B. OLSZOWSKI, Universal algorithm for generation of matrices used in dynamics of circular Timoshenko segments, Engng. Trans., 40, 2, 213-228, 1992.
K.C. PARK and D.L. FLAGGS, A Fourier analysis of spurious mechanisms and locking in the finite element method, Camp. Meth. Appl. Mech. Engng, 46, 65-81, 1984.
L. MEIROVITCH, M.K. KWAK, On the convergence of the classical Rayleigh-Ritz method and the finite element method, AIAA J., 28, 8, 1509-1516, 1990.
H.BARUH, S.S.K. TADIKONDA, Another look at admissible functions, J. Sound Vibr., 132, 1, 73-87, 1989.
B.OLSZOWSKI, Free in-plane vibrations of unsupported circular rings. Part I. Natural frequencies [in Polish], Engng. Trans., 37, 3, 547-563, 1989; Part II. Natura/modes [in Polish], Engng. Trans., 38, 3-4, 185-202, 1990; Part III. Free single Frequency vibrations [in Polish], Engng. Trans., 38, 3-4, 203-219, 1990.
B. OLSZOWSKI, Universal algorithm for generation of matrices used in dynamics of circular Timoshenko segments, Engng. Trans., 40, 2, 213-228, 1992.
