Laminated beams with viscoelastic interlayer

We analytically solve the time-dependent problem of a simply-supported laminated beam, composed of two elastic layers connected by a viscoelastic interlayer, whose response is modeled by a Prony’s series of Maxwell elements. This case applies in particular to laminated glass, a composite made of glass plies bonded together by polymeric films. A practical way to calculate the response of such a package is to consider also the interlayer to be linear elastic, assuming its equivalent elastic moduli to be the relaxed moduli under constant strain, after a time equal to the duration of the design action. The obtained results, that are confirmed by a full 3-D viscoelastic finite-element numerical analysis, emphasize that there is a noteworthy difference between the state of strain and stress calculated in the full-viscoelastic case or in the aforementioned “equivalent” elastic problem.