Vibration of circular Mindlin plates with concentric elastic ring supports

This paper studies the vibration behaviour of circular Mindlin plates with multiple concentric elastic ring supports. Utilizing the domain decomposition technique, a circular plate is divided into several annular segments and one core circular segment at the locations of the elastic ring supports. The governing differential equations and the solutions of these equations are presented for the annular and circular segments based on the Mindlin-plate theory. A homogenous equation system that governs the vibration of circular Mindlin plates with elastic ring supports is derived by imposing the essential and natural boundary and segment interface conditions. The first-known exact vibration frequencies for circular Mindlin plates with multiple concentric elastic ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the elastic ring support stiffness, locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed.