Vibration of a Circular Arc Bar in its Plane : Both Ends Built-in

Abstract

The Lagrangian in the vibration of a circular arc bar in its plane is discussed and the radial and tangential displacements are obtained in general forms. The frequency equations of a circular ring and a circular arc bar with hinged ends for the vibration in its plane are obtained and they are compared with the already known solutions. Then, the frequency equations of a circular arc bar with both ends built-in are obtained from the Lagrangian and the nondimensional frequencies are shown in figures. Also, for the vibration of a circular arc bar with free ends, the nondimensional frequencies are calculated and are shown in figures.