Free vibration analysis of sandwich beam with a viscoelastic core based on the extended high-order sandwich panel theory approach is presented. The effects of transverse shear and core compressibility are of high importance in sandwich structures, having an influence on the entire structural behavior especially in vibrations. For applications involving stiffer cores, the high-order sandwich panel theory (HSAPT) cannot accurately predict the shear and axial stress distributions in the core. Thus, by using the “Extended High-Order Sandwich Panel Theory” (EHSAPT), the in-plane rigidity of the core is considered in addition to the compressibility of the core in the transverse direction. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core, and the rotation at the centroid of the core) instead of just one (mid-point transverse displacement) commonly adopted in other available theories. The mathematical formulation uses the Hamilton principle and includes derivation of the governing equations along with the appropriate boundary conditions. The formulation uses the classical thin plate theory for the face sheets and a two-dimensional elasticity theory or equivalent one for the core. In addition, Young modulus, rotational inertia, and kinetic energy of the core are considered and core is assumed as an orthotropic viscoelastic material. The analysis is applicable for any types of loading scheme, localized as well as distributed, and distinguish between loads applied at the upper or the lower face. The obtained results are compared with recent research published by the present authors which was done numerically by using FEM on viscoelastic sandwich beam and the corresponding results of other previous researches. The influence of material properties, face layup and geometry effect on natural frequencies of composite sandwich beams are investigated.

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