Out-of-Plane Free Vibration Analysis of a Horizontally Circular Curved Beam Carrying Arbitrary Sets of Concentrated Elements

Abstract

For convenience, a horizontally circular curved beam without any attachments is called a “bare” curved beam and the one carrying any attachments is called a “loaded” curved beam, in this paper. For the out-of-plane free vibrations of bare curved beams, one can find some exact solutions from the existing literature, but this is not true for those of the loaded curved beams. One of the main reasons for the last situation is due to the difficulty of solving a complex-variable eigenvalue equation. It is well known that the half-interval method is one of the simplest techniques for searching the roots of an eigenvalue equation. However, it suffers difficulty if the eigenvalue equation is a determinant form