Natural frequencies of circular arcs with varying cross section

This paper presents a transter matrix method for conveniently predicting the natural frequencies of circular arcs with varying cross section. The equations of in-plane vibration of an arc are written as a coupled set of first-order differential equations by using the transfer matrix of the arc. Once the transfer matrix has been determined, the natural frequencies and the mode shapes of the vibration are calculated in terms of the elements of the matrix for a given set of boundary conditions at the ends of the arc. The numerical results obtained by the method are compared with the experimental results for free-clamped arcs with tapered breadth, which are in good agreement with each other.