In this study, a sandwich structure added with two viscoelastic adhesive layers on both sides of the core and face sheets was considered.The analytical formulations of the displacement, stress and strain on each
layer of the structure were derived by proposed geometric assumption and
continuity conditions between layers. Then the governing equation of
equilibrium was obtained by the Euler-Ostrogradskii equation. Finally, a
numerical case study was adopted to conduct the validation of the modeling
by comparing the results between the viscoelastic analytical solutions and
the viscoelastic finite element method (FEM) solutions. It can be proved
that the elastic analytical or the FEM solutions without counting the
adhesive layers cannot perform realistic mechanical responses of the
sandwich structure. The present viscoelastic model is also compared with
the previous elastic five–layer model of Huang [7]. The comparison verifies the validity of the present model, and this model could be the expansion of the previous elastic model. Consequently, the effect of adhesive thickness in sandwich beam on its viscoelastic property was analyzed, by which we can conclude that the viscoelastic adhesive layers must be involved into the stress-strain state analysis of sandwich beam.