Free vibration of thin circular rings on periodic radial supports

Natural frequencies and normal modes are obtained for in-plane, inextensional vibrations of a thin circular ring with equi-spaced, identical radial supports. A wave approach is used. Natural frequencies are determined from the propagation constants of the ring by considering it as an endless periodic structure. Normal modes are obtained by superposition of a pair of opposite-going free wave groups. Numerical results have been presented for both rigid and circumferentially guided supports. It has been shown that at certain frequencies two different natural modes can exist. This has been verified experimentally.