Vibration of Thin Rectangular Plates with Mixed Boundary Conditions along the Edges

This paper presents a novel analytical method for determining the vibration frequencies of rectangular plates with mixed boundary conditions along their edges. Building on a recently derived exact solution that is applicable to all boundary condition configurations, this approach extends its applicability to cases with varying edge constraints. The problem is formulated as an assembly of interconnected plate segments, with continuity enforced along shared edges as an integral part of the solution. To validate the method’s accuracy, its results are compared with published findings from alternative approaches, highlighting its effectiveness in handling complex boundary conditions. The possibility of adjusting the natural frequencies by mixing edge restraints to obtain a desired value is presented. A wide range of mixed boundary configurations can be explored, and representative examples are provided.