Free vibration analysis of stepped circular Mindlin plates

This paper presents the first-known investigation on exact vibration of circular Mindlin plates with multiple step-wise thickness variations. A stepped circular plate is divided into multiple annular and one circular segments along the locations of the step variations. The governing differential equations for harmonic vibration of annual and circular segments are derived and an analytical method based on the domain decomposition technique is developed to solve the plate vibration problem. Exact vibration solutions are presented for circular Mindlin plates of different edge support conditions and various combinations of step-wise thickness variations. The influence of plate boundary conditions, plate thickness ratios, step location ratios and step thickness ratios on the vibration behaviour of stepped circular Mindlin plates are examined. The exact vibration results can serve as benchmark values for researchers to validate their numerical methods for such circular plate problems.