Accurate free vibration analysis of thick laminated circular plates with attached rigid core

This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin's first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis.

► Derivation of equations of laminated circular plates with attached rigid core. ► Obtaining boundary conditions of up-down translation and wobbly rotation of core. ► Explicit solution of governing equations without any usage of approximate methods. ► Study of the effects of the core on frequency parameters of laminated structures. ► Accurate frequencies are presented for a wide range of plate and core parameters.