Vibration of a Circular Arc Bar : Perpendicular to its Plane

Abstract

The vibration of a circular arc bar which occurs perpendicularly to its plane is studied. Its Lagrangian is obtained and from the condition to minimize it, frequency equations and boundary values can be obtained. For a circular ring and a circular arc bar with both ends built-in, the frequency equations obtained by the method mentioned above are compared with the known ones. For a circular arc bar with both ends free, the frequency equations and the boundary values are obtained and some frequencies are calculated and given in graphs. Also, it is ascertained that the centre of gravity of the circular arc bar does not move during the vibration.