In-plane vibration analyses of circular arches by the generalized differential quadrature rule

In-plane free vibrations of circular arches are investigated using the generalized differential quadrature rule (GDQR) proposed recently. The Kirchhoff assumptions for thin beams are considered, and the neutral axis is taken as inextensible. Several examples of arches with uniform, continuously varying, and stepped cross-sections are presented to illustrate the validity and accuracy of the GDQR. The necessary domain decomposition technique is used for some cases. The obtained frequencies are compared with those calculated from a number of other approaches from the Rayleigh–Ritz, Rayleigh–Schmidt and Galerkin methods to the finite element technique and the cell discretization method. The GDQR frequencies are always greater than those obtained from the cell discretization method that produces the lower bounds to the exact results, and are also in agreement with the upper bounds to the exact results.