Free vibrations of shear-flexible and compressible arches by FEM

The purpose of this paper is to analyse free vibrations of arches with in0uence of shear and axial forces taken into account. Arches with various depth of cross-section and various types of supports are considered. In the calculations, the curved >nite element elaborated by the authors is adopted. It is the plane two-node, six-degree-of-freedomarch element with constant curvature. Its application to the static analysis yields the exact results, coinciding with the analytical ones. This feature results fromthe use of the exact shape functions in derivation of the element sti@ness matrix. In the free vibration analysis the consistent mass matrix is used. It is obtained on the base of the same functions. Their coeAcients contain the in0uences of shear 0exibility and compressibility of the arch. The numerical results are compared with the results obtained for the simple diagonal mass matrix representing the lumped mass model. The natural frequencies are also compared with the ones for the continuous arches for which the analytically determined frequencies are known. The advantage of the paper is a thorough analysis of selected examples, where the in0uences of shear forces, axial forces as well as the rotary and tangential inertia on the natural frequencies are examined