Free vibration of circular arches
Pereira, Carlos Antonio Lopes
Austin, Walter J.
Master of Science
The lower natural frequencies and the associated modes of vibration of uniform circular arches which are either fixed or simply supported at the ends are computed and studied in this thesis. A general theory which considers the effects of rotatory inertia and shearing deformations as well as extensional and flexural deformations was used. When both rotatory inertia and shearing deformations are neglected the general theory reverts to a well-known classical theory which is based upon the same assumptions as Flugge's theory for the bending of cylindrical shells. The governing differential equations were solved numerically by a Holzer -type iterative procedure combined with an initial value integration method. A Runge-Kutta integration technique was used. The method was programmed for an IBM 7040 computer, and all results were obtained on this computer. A detailed study has been made of the lowest ten vibration frequencies and modes for fixed arches for a wide range of slenderness ratios and for angles of opening of 45° , 90° and 180°, using the classical theory. The effects of rotatory inertia and shearing deformations have been investigated only for arches with an angle of opening of 90°. Simple approximate expressions for estimating the natural frequencies of fixed-ended arches (classical theory) are developed and their accuracy evaluated by comparing them with the results obtained by exact analysis. In addition, exact solutions of classical theory were made for hinged circular arches with angles of opening of 45° and 180° and the accuracy of approximate expressions for estimating the natural frequencies of hinged arches proposed by Austin, Veletsos and Wung were evaluated for these angles of opening.