Analytical modeling of multilayered dynamic sandwich composites embedded with auxetic layers

The influence of viscoelastic and auxetic (Negative Poisson's Ratio NPR) layers on the free vibration modeling of a composite sandwich structure is analyzed in this work. For such purpose, an analytical formulation is performed based on the specification of kinematic theories in terms of displacement fields within each layer of the structure. For instance, simple theories like classical laminate theory (CLT) and high order shear deformation theory (HSDT) are considered. This enables the definition of a dynamic problem for 5-layered sandwich composite using the principle of virtual displacement. Moreover, modal parameters in terms of natural frequencies and associate loss factors are given through the transversal displacement. For linear and isotropic layers, numerical applications highlight the result of the Poisson's ratio on the modal responses. It is particular observed that the natural frequency and loss factor show an increase with respect to the auxeticity of the viscoelastic layers while no significant variations related to the shear function are noticed from one theory to another.