Vibration of hinged circular arches

The governing differential equations for the vibration of uniform circular arches have been derived considering in addition to the usual actions the effect of rotatory inertia and shear de-formation. A trial eigenvalue method is used for determining the natural frequencies and mode shapes. The Runge-Kutta fifth order integration technique is used in this method to perform the integration of the differential equations. A detailed study has been made of the lowest eight vibration frequencies for a hinged arch with an angle of opening equal to ninety degrees. The effect of slenderness ratio and the influences of the rotatory inertia and shear deformation on frequencies are presented in detail in tables and curves. It is shown that the frequencies found neglecting shear and rotatory inertia can be considered in most regions to be either primarily extensional or flexural but that a coupling exists in certain transition regions. The effects of shear deformation and rotatory inertia, which are most important in and near the transition regions, are to smooth the frequency curves