Vibrational characteristics are obtained for a rotating ring with equi-spaced elastic supports by using the wave approach. Especially, the variation of the natural frequencies with the rotating speed and the number of elastic supports is investigated. Each elastic support is idealized as a combination of concentrated tangential, rotational and radial stiffnesses acting at the mid-plane of the ring. In the wave approach, state variables at the support A;
UA are related to the adjacent support B;
UB as
UB=
eμUA where the complex μ(=μ
R+
iμ
I) is the so-called propagation constant. The real part (μ
R) and the imaginary part (μ
I) of the constant μ are the measures of the rate of decay and the change of phase over the distance between the adjacent supports for travelling wave, respectively. It should be noted that, if the real part: μ
R is not equal to zero, the travelling wave is attenuated and the energy flow does not exist. The frequency reigions where μ
R≠0 are called stopping bands while the frequency reigions where μ
R=0 are called passing bands. And the natural frequency is determinied by the condition that, for the propagation of wave once around the whole ring through
N supports, the propagation constant satisfies an equality μ
N=2π
j(
j an integer). Numerical results show the effects of rotational speed and the number of elastic supports on the propagation constants which characterize the frequency reigions as either a stopping band or a passing band. And the relation of the natural frequencies with the propagation constants is discussed.
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