Elasticity solution of two-layer beam with a viscoelastic interlayer considering memory effect

The elasticity solution of a simply supported beam, composed of two same elastic layers adhesively bonded by a thin viscoelastic interlayer, subjected to time-dependent load is studied. The tangential and transverse strains in the interlayer are considered simultaneously. The viscoelasticity of the interlayer is described by the standard linear model, which considers the memory effect of strains. An analytical method is developed to obtain the stress and displacement fields in the beam. The present method gives the exact stress and displacement distributions in the beam, which cannot be predicted by the approximate theories such as the one-dimensional Euler–Bernoulli theory. The comparison study indicates that the present results have a good agreement with the two-dimensional finite element solutions. However, there is considerable difference between the present solution and the Euler–Bernoulli solution for thick beams. It is shown that the effect of transverse strains of the interlayer on displacements and stresses cannot be neglected for thick beams and the common quasi-elastic interlayer model is unserviceable for beams with viscoelastic interlayer with the repeatedly loading-unloading path. Finally, the effects of interlayer thickness and viscoelastic properties on displacements and stresses of the beam are discussed in detail.