Abstract
The early investigators into the in-plane vibration of rings were Hoppe $Hoppe ^{1)}$ and $Love ^{2)}$. $Love ^{2)}$ Improved on Hoppe's theory by allowing for stretching of the ring. $Lamb ^{3)}$ investigated the statics of incomplete ring with various boundary conditions and the dynamics of an incomplete free-free ring of small curvature. Den $Hartog ^{4)}$ used the Rayleigh-Ritz method for finding the lowest natural frequency of circular arcs with simply supported or clamped ends and his work was extended by Volterra and $Morell ^{5)}$ for the vibrations of arches having center lines in the form of cycloids, catenaries or parabolas.(omitted)