Exact and approximate dynamic analysis of circular arches using DQM

equation of motion governing free in-plane inextensional vibrations of circular arches (see Henrych, 1981). All the boundary conditions can be imposed exactly, without introducing d points (see e.g. Bert and Malik, 1996). Consequently, the results are calculated with high precision, and a comparison between exact and approximate frequencies becomes possible. The convergence rate of the discretization method is shown to be very fast, even for the higher eigenvalues, so that a small number of Lagrangian coordinates permits a good approximation to the true results. It is shown that the approximate formulation leads to noticeable errors for the ®rst frequencies of deep arches, whereas shallow arches and higher-order frequencies can be safely calculated with the simpli®ed approach. The paper ends with some tables in which the ®rst ten free vibrations frequencies for clamped arches, two-hinged arches and cantilever arches are compared with some known results from the literature