Blast loads and nonlinear vibrations of laminated glass plates in an enhanced shear deformation theory

The nonlinear dynamic response of a laminated glass plate under the pressure generated by a blast wave, described via the Friedlander's model, is investigated. In order to account for the heterogeneity of the laminated package, composed by two glass plies sandwiching a thin and soft polymeric interlayer, a geometrically nonlinear, third-order shear deformation theory with rotary inertia is used. Within the quasi-elastic approximation, the constitutive response of the polymer is described by its secant elastic moduli for short-term loading at room temperature, while the dissipation associated with its viscosity is taken into account through an equivalent effective damping. The problem is discretized by a reduced-order model retaining 40 degrees of freedom and the first four vibration modes, which are the ones receiving most of the energy from the blast. A geometrically nonlinear damping model is introduced to simulate the increase in damping associated with large-amplitude oscillations of the plate, which results from the interaction between the large deflections of the glass plies and the viscosity of the interlayer. Forced nonlinear vibrations around the frequency of the fundamental mode are also investigated, to complete the study of the nonlinear dynamics. The results highlight the importance of the nonlinear effects of damping, which can almost halve the deformations and stresses in laminated glass with respect the linear case at high levels of excitation, while still remaining within the limits of material strengths.