Free Vibrations Of Circular Arches: A Review

In this paper a critical brief review of the free dynamics of circular arches is presented, under the classical hypotheses that (1) the dimensions of the cross-section are small in comparison with the radius, (2) the axis is inextensible and (3) shear forces and rotatory inertia are neglected. A simple—yet efficient—method is proposed, which allows one to take into account quite naturally the cross-section variations and the presence of flexible supports. A number of other approaches are also briefly illustrated, from the Ritz and Galerkin methods to the finite element techniques, and their numerical performances are compared for a wide range of examples. Uniform arches with rotationally flexible and axially flexible supports have been extensively examined, together with three different kinds of stepped arches and two different arches with linearly varying cross-section. Whenever possible, a comparison with available exact solutions is also performed. The agreement among all these methods is generally good, even if there are some theoretical discrepancies to be pointed out. Copyright 1994, 1999 Academic Press