Chapter 12 – Free Vibration Relationships

This chapter explores the relationships between the natural frequencies of the classical Kirchhoff plate theory, the Mindlin plate theory, and the Reddy plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies provides the solutions of the shear deformable plate theories from the known Kirchhoff plate theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship. The relationships may also be used for symmetrically, isotropic laminated plates by modifying appropriately the stiffnesses. Unlike the FSDT-CPT frequency relationship, the TSDT-CPT frequency relationship does not need a shear correction factor. This feature is advantageous when considering laminated plates where the shear correction factor is not available.