Free vibration analysis of sandwich plates with non-monotonically graded flexible core is studied using a high-order sandwich panel theory. The non-monotonically graded flexible core is considered as two monotonically graded flexible core layers. In this high-order theory, the first-order shear deformation theory is used for the face sheets and a 3D-elasticity solution of weak core is employed for each single core layer. The laminated two-layered core is analyzed and formulated by the mixed layer-wise theory. Based on the continuity of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are derived by Hamilton’s principle. The accuracy of the present approach is validated by comparing with the numerical results obtained from finite element method and good agreements are reached. Parametric study is also conducted to investigate the effect of distribution of functionally graded material properties, the monotonically graded core thickness ratio, and the thickness-to-side ratio on the vibration frequency.
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