Vibrations of Elastically Connected Ring Systems

A study on free inextensional vibrations of two elastically connected ring systems and of single rings are presented. Equations of motion for a double-ring system are derived and solutions to complete and incomplete ring systems are obtained. The solutions for the complete ring systems are exact and are expressed in terms of trigonometric functions. For a semicircular single ring with clamped ends the frequencies are calculated on the basis of an exact method and for simple supported rings the values are obtained by the method of Lagrangean Multipliers. For semicircular double-ring systems the frequencies are calculated by the use of Rayleigh-Ritz method. Free vibration experiments were conducted on systems of full rings and on ring segments. Experimental results are compared with theoretical values and have been found to be in good agreement.