A high-order theoretical approach for the free-vibration analysis of delaminated unidirectional sandwich panels with a compressible core is presented. The analytical approach accounts for the flexibility of the core in the vertical direction and the resulting high-order displacement, acceleration, and velocity fields within the core. The existence of delaminated regions along the sandwich panel and the various interfacial stress transfer conditions at the delaminated core-face interface are considered and studied. The analytical model developed in the article is applicable to any type of boundary conditions including different support conditions at the same section. The derivation of the model uses Hamilton's variational principle as well as the beam and lamination theories for the face-sheets and two-dimensional elasticity theory for the modeling of the core. The free-vibration problem is formulated and solved assuming a harmonic behavior in time and using the multiple shooting method along with the Newton—Raphson scheme for the solution in space. Numerical results that emphasize the influence of the boundary conditions, the effect of the delaminated regions, the influence of the contact conditions within the debonded region, and the high-order effects through the depth of the core are presented and discussed. The model and the solution procedure are verified through a comparison with finite elements analyses and with an analytical solution that is based on the Modified Galerkin method. The article closes with a summary and conclusions.
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