Free flexural axisymmetric vibration of a clamped circular sandwich plate with a functionally graded core

This study presents an analytical model of a clamped circular sandwich plate with a functionally graded core, developed within the framework of an individual nonlinear shear deformation theory. The mathematical formulation is an original contribution, providing a unified representation of various structural configurations -- including three-layer-like, five-layer-like, homogeneous single-layer, and intermediate forms -- through a single continuous function. The variation of Young's modulus across the core is controlled by three parameters, enabling flexible modeling of material gradation. The governing equations are derived using Hamilton's principle and are solved analytically through an approximate solution method. The proposed model allows investigation of the effects of material property variation and the core-to-plate thickness ratio on the fundamental natural frequency, as well as on the shear effect coefficient and plate mass, yielding general conclusions supported by a coherent theoretical framework.