Levy solutions for vibration of multi-span rectangular plates

This paper presents the Levy method to investigate the vibration behaviour of multi-span rectangular plates. The Levy method is applicable and analytical for rectangular plates with at least two parallel simply supported edges. The continuity at an interface between two spans is maintained by imposing both the essential and natural boundary conditions along the interface. The impact of the internal line supports on the vibration behaviour of the plates is investigated by varying both the number of internal lines and the line positions. Results for the vibration of two- and three-span rectangular plates are presented, in which the first-known exact solutions for plates involving free edges are included. The present results may serve as benchmark solutions for such plates.