Exact vibration solutions for circular Mindlin plates with multiple concentric ring supports

This paper presents an analytical approach to investigate the vibration behaviour of circular Mindlin plates with multiple concentric ring supports. A circular plate is first divided into multiple annular segments and a circular segment at the locations of the ring supports. The governing differential equations and the solutions of these equations for the annular and circular segments based on the Mindlin plate theory are presented. A homogenous equation system governing the vibration of circular Mindlin plates with 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 ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the ring support locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed