This work is to study parametric vibration of a dual-ring structure through analytical and numerical methods by focusing on the relationships between basic parameters and parametric instability. An elastic dual-ring model is developed by using Lagrange method, where the radial and tangential deflections are included, and motionless and moving supports are also incorporated. Analytical results imply that there are four kinds of parametric excitations, and the numerical results show that there exist stable and unstable areas separated by transition curves or straight lines, and even crossover points. The relationships are determined as simple expressions in basic parameters, including discrete stiffness number and wavenumber. Whether the parametric resonance can be excited or not depends on the values of support stiffness, rotating speed, and natural frequency. Vibrations at the crossover points are also addressed by using the multiscale method. Comparisons against the available results regarding ring structures with moving supports are also made. Extensions of this study, including the use of powerful Sinha method to deal with the parametric vibration, are suggested.

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