THE EFFECT OF SHEAR DEFORMATION ON THE VIBRATION OF CIRCULAR ARCHES BY THE FINITE-ELEMENT METHOD

The free-vibration natural frequencies of circular arches subtending a considerable range of central angles and having a wide range of ratios of radius of curvature to radius of gyration (R/r) are obtained. Both symmetrical and antisymmetrical modes of vibration are investigated and the crossover values of frequencies from one of the modes to the other are obtained. Arches that ar e fixed at both ends, hinged at both ends and one end fixed whilst the other is pinned are analysed. The finite element method is employed to obtain these results. A strain-based curved beam element, using Timoshenko's deep-beam formulation in a system of curvilinear coordinates, is obtained and employed in the analysis. It is shown that this element does not have any spurious constraints and locking characteristics. Convergence curves show that accurate and stable results are obtained by the use of few elements, enabling the employment of a simple method of obtaining the eigenvalues and eigenvectors representing the frequencies and the corresponding modes of vibrations, respectively.